theorem cbvpim {x y: nat} (p1 q1: wff x) (p2 q2: wff y): $ x = y -> (p1 <-> p2) $ > $ x = y -> (q1 <-> q2) $ > $ (P. x p1 -> q1) <-> (P. y p2 -> q2) $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv | F/ y p1 |
|
2 | nfv | F/ y q1 |
|
3 | nfv | F/ x p2 |
|
4 | nfv | F/ x q2 |
|
5 | hyp e1 | x = y -> (p1 <-> p2) |
|
6 | hyp e2 | x = y -> (q1 <-> q2) |
|
7 | 1, 2, 3, 4, 5, 6 | cbvpimh | (P. x p1 -> q1) <-> (P. y p2 -> q2) |