Theorem chvar 1986

Description: Implicit substitution of y for x into a theorem. (Contributed by Raph Levien, 9-Jul-2003.) (Revised by Mario Carneiro, 3-Oct-2016.)

Hypotheses

Ref	Expression
chvar.1	|- F/xps
chvar.2	|- (x = y -> (ph <-> ps))
chvar.3	|- ph

Assertion

Ref	Expression
chvar	|- ps

Proof of Theorem chvar

Step	Hyp	Ref	Expression
1		chvar.1	. . 3 |- F/xps
2		chvar.2	. . . 4 |- (x = y -> (ph <-> ps))
3	2	biimpd 198	. . 3 |- (x = y -> (ph -> ps))
4	1, 3	spim 1975	. 2 |- (A.xph -> ps)
5		chvar.3	. 2 |- ph
6	4, 5	mpg 1548	1 |- ps

Syntax hints:   -> wi 4   <-> wb 176   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  csbhypf  3172  opelopabsb  4698