Theorem chv 984

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
chv	|- ps

Distinct variable group(s):   ps,x

Proof of Theorem chv

Step	Hyp	Ref	Expression
1		chv.1	. . 3 |- (x = y -> (ph <-> ps))
2	1	a4b1 928	. 2 |- (A.xph -> ps)
3		chv.2	. 2 |- ph
4	2, 3	mpg 684	1 |- ps

Syntax hints:   -> wi 2   <-> wb 127   = weq 797

This theorem is referenced by:  hblem 1170  so 2152

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-9 799  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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