Theorem chvarv 1809

Description: Implicit substitution of y for x into a theorem. (Contributed by NM, 20-Apr-1994.)

Hypotheses

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

Assertion

Ref	Expression
chvarv	|- ps

Distinct variable group:   ps,x

Allowed substitution hints:   ph(x,y)   ps(y)

Proof of Theorem chvarv

Step	Hyp	Ref	Expression
1		chv.1	. . 3 |- (x = y -> (ph <-> ps))
2	1	spv 1737	. 2 |- (A.xph -> ps)
3		chv.2	. 2 |- ph
4	2, 3	mpg 1337	1 |- ps

Syntax hints:   -> wi 4   <-> wb 98

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-17 1416  ax-i9 1420  ax-ial 1424

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

This theorem is referenced by:  axext3  2020  axsep2  3867  tz6.12f  5145  tfrlem3-2  5868  bdsep2  9320  strcoll2  9413