Theorem chvarv 1712

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 1649	. 2 |- (A.xph -> ps)
3		chv.2	. 2 |- ph
4	2, 3	mpg 1332	1 |- ps

Syntax hints:   -> wi 3   <-> wb 163   = wceq 1298

This theorem is referenced by:  axext3 1867  hblemOLD 1994  axrep1 3429  so 3620  isgrp2i 9360  inposet 14620  sdc 15811  fdc 15812  fdc1 15813  iscringd 16147

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-17 1317  ax-4 1319  ax-5o 1321  ax-9o 1481

This theorem depends on definitions:  df-bi 164

Copyright terms: Public domain