Theorem chvar 1637

Description: Implicit substitution of y for x into a theorem. (Contributed by Raph Levien, 9-Jul-2003.) (Revised by Mario Carneiro, 3-Oct-2016.)

Hypotheses

Ref	Expression
chvar.1	|- F/xps
chvar.2	|- (x = y -> (ph <-> ps))
chvar.3	|- ph

Assertion

Ref	Expression
chvar	|- ps

Proof of Theorem chvar

Step	Hyp	Ref	Expression
1		chvar.1	. . 3 |- F/xps
2		chvar.2	. . . 4 |- (x = y -> (ph <-> ps))
3	2	biimpd 132	. . 3 |- (x = y -> (ph -> ps))
4	1, 3	spim 1623	. 2 |- (A.xph -> ps)
5		chvar.3	. 2 |- ph
6	4, 5	mpg 1337	1 |- ps

Syntax hints:   -> wi 4   <-> wb 98   F/wnf 1346

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-i9 1420  ax-ial 1424

This theorem depends on definitions:  df-bi 110  df-nf 1347

This theorem is referenced by:  csbhypf  2879  opelopabsb  3988  findes  4269  fvmptssdm  5198  dfoprab4f  5761  dom2lem  6188  uzind4s  8309