Theorem chvarv 1997

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 1913	. 2 |- ( A. x ph -> ps )
3		chv.2	. 2 |- ph
4	2, 3	mpg 1504	1 |- ps

This proof depends on syntax axioms:   -> wi 4   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587

This proof depends on definitions:  df-bi 117  df-nf 1514

This theorem is used by:  axext3  2221  axsepg  4250  tz6.12f  5724  ltordlem  8810  bdsep2  16912  strcoll2  17009