Step |
Hyp |
Ref |
Expression |
0 |
|
cA |
|- A |
1 |
|
cB |
|- B |
2 |
0 1
|
ctxp |
|- ( A (x) B ) |
3 |
|
c1st |
|- 1st |
4 |
|
cvv |
|- _V |
5 |
4 4
|
cxp |
|- ( _V X. _V ) |
6 |
3 5
|
cres |
|- ( 1st |` ( _V X. _V ) ) |
7 |
6
|
ccnv |
|- `' ( 1st |` ( _V X. _V ) ) |
8 |
7 0
|
ccom |
|- ( `' ( 1st |` ( _V X. _V ) ) o. A ) |
9 |
|
c2nd |
|- 2nd |
10 |
9 5
|
cres |
|- ( 2nd |` ( _V X. _V ) ) |
11 |
10
|
ccnv |
|- `' ( 2nd |` ( _V X. _V ) ) |
12 |
11 1
|
ccom |
|- ( `' ( 2nd |` ( _V X. _V ) ) o. B ) |
13 |
8 12
|
cin |
|- ( ( `' ( 1st |` ( _V X. _V ) ) o. A ) i^i ( `' ( 2nd |` ( _V X. _V ) ) o. B ) ) |
14 |
2 13
|
wceq |
|- ( A (x) B ) = ( ( `' ( 1st |` ( _V X. _V ) ) o. A ) i^i ( `' ( 2nd |` ( _V X. _V ) ) o. B ) ) |