Theorem chvarv 1854

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 1782	. 2 |- ( A. x ph -> ps )
3		chv.2	. 2 |- ph
4	2, 3	mpg 1381	1 |- ps

Syntax hints:   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468

This theorem depends on definitions:  df-bi 115  df-nf 1391

This theorem is referenced by:  axext3  2065  axsep2  3899  tz6.12f  5228  bdsep2  10820  strcoll2  10921