Theorem chvarvOLD 2264

Description: Obsolete proof of chvarv 2263 as of 14-Jul-2021. (Contributed by NM, 20-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Apr-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
chvarvOLD	|- ps

Distinct variable group:   ps, x

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

Proof of Theorem chvarvOLD

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ x ps
2		chvarv.1	. 2 |- ( x = y -> ( ph <-> ps ) )
3		chvarv.2	. 2 |- ph
4	1, 2, 3	chvar 2262	1 |- ps

Syntax hints:   -> wi 4   <-> wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)