:: SCHEMS_1 semantic presentation

scheme :: SCHEMS_1:sch 4
s4{ P1[ set ] } :
ex a being set st P1[a]
provided
E6: for a being set holds P1[a]
proof end;

scheme :: SCHEMS_1:sch 7
s7{ P1[ set , set ] } :
for b being set ex a being set st P1[a,b]
provided
E6: ex a being set st
for b being set holds P1[a,b]
proof end;

scheme :: SCHEMS_1:sch 10
s10{ P1[ set ], P2[ set ] } :
( ( for a being set holds P1[a] ) implies for a being set holds P2[a] )
provided
E6: for a being set st P1[a] holds
P2[a]
proof end;

scheme :: SCHEMS_1:sch 12
s12{ P1[ set ], P2[ set ] } :
( ( for a being set holds P1[a] ) iff for a being set holds P2[a] )
provided
E6: for a being set holds
( P1[a] iff P2[a] )
proof end;

scheme :: SCHEMS_1:sch 14
s14{ P1[ set ], P2[] } :
( ( for a being set holds P1[a] ) implies P2[] )
provided
E6: for a being set st P1[a] holds
P2[]
proof end;

scheme :: SCHEMS_1:sch 16
s16{ P1[ set ], P2[ set ] } :
ex a being set st
for b being set holds
( P1[a] or P2[b] )
provided
E6: ( ex a being set st P1[a] or for b being set holds P2[b] )
proof end;

scheme :: SCHEMS_1:sch 18
s18{ P1[ set ], P2[ set ] } :
( ex a being set st P1[a] or for b being set holds P2[b] )
provided
E6: ex a being set st
for b being set holds
( P1[a] or P2[b] )
proof end;

scheme :: SCHEMS_1:sch 19
s19{ P1[ set ], P2[ set ] } :
ex a being set st
for b being set holds
( P1[a] or P2[b] )
provided
E6: for b being set ex a being set st
( P1[a] or P2[b] )
proof end;

scheme :: SCHEMS_1:sch 20
s20{ P1[ set ], P2[ set ] } :
for b being set ex a being set st
( P1[a] & P2[b] )
provided
E6: ( ex a being set st P1[a] & ( for b being set holds P2[b] ) )
proof end;

scheme :: SCHEMS_1:sch 21
s21{ P1[ set ], P2[ set ] } :
( ex a being set st P1[a] & ( for b being set holds P2[b] ) )
provided
E6: for b being set ex a being set st
( P1[a] & P2[b] )
proof end;

scheme :: SCHEMS_1:sch 24
s24{ P1[ set ], P2[ set ] } :
ex a being set st
for b being set holds
( P1[a] & P2[b] )
provided
E6: for b being set ex a being set st
( P1[a] & P2[b] )
proof end;

scheme :: SCHEMS_1:sch 25
s25{ P1[ set , set ] } :
ex b being set st
for a being set holds P1[a,b]
provided
E6: for a, b being set holds P1[a,b]
proof end;

scheme :: SCHEMS_1:sch 26
s26{ P1[ set , set ] } :
ex a being set st P1[a,a]
provided
E6: ex a being set st
for b being set holds P1[a,b]
proof end;

scheme :: SCHEMS_1:sch 27
s27{ P1[ set , set ] } :
for a being set ex b being set st P1[b,a]
provided
E6: for a being set holds P1[a,a]
proof end;

scheme :: SCHEMS_1:sch 28
s28{ P1[ set , set ] } :
for a being set ex b being set st P1[a,b]
provided
E6: for a being set holds P1[a,a]
proof end;

scheme :: SCHEMS_1:sch 29
s29{ P1[ set , set ] } :
ex a, b being set st P1[a,b]
provided
E6: for b being set ex a being set st P1[a,b]
proof end;