Theorem cbvalvOLD 2274

Description: Obsolete proof of cbvalv 2273 as of 17-Jul-2021. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

Ref	Expression
cbvalvOLD	|- ( A. x ph <-> A. y ps )

Distinct variable groups:   ph, y   ps, x

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

Proof of Theorem cbvalvOLD

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ y ph
2		nfv 1843	. 2 |- F/ x ps
3		cbvalv.1	. 2 |- ( x = y -> ( ph <-> ps ) )
4	1, 2, 3	cbval 2271	1 |- ( A. x ph <-> A. y ps )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481

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-10 2019  ax-11 2034  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)