Theorem chvarv 1329

Description: Implicit substitution of y for x into a theorem.

Hypotheses

Ref	Expression
chv.1	|- (x = y -> (ph <-> ps))
chv.2	|- ph

Assertion

Ref	Expression
chvarv	|- ps

Distinct variable group:   ps,x

Proof of Theorem chvarv

Step	Hyp	Ref	Expression
1		chv.1	. . 3 |- (x = y -> (ph <-> ps))
2	1	a4v 1274	. 2 |- (A.xph -> ps)
3		chv.2	. 2 |- ph
4	2, 3	mpg 988	1 |- ps

Syntax hints:   -> wi 3   <-> wb 146   = wceq 958

This theorem is referenced by:  hblem 1567  axrep1 2699  so 2870  isgrp2i 8072  inposet 10477

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977  ax-9o 1125

This theorem depends on definitions:  df-bi 147

Copyright terms: Public domain