Theorem bj-cbval2vv 32739

Description: Version of cbval2v 2285 with a dv condition, which does not require ax-13 2246. (Contributed by BJ, 16-Jun-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-cbval2vv.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )

Assertion

Ref	Expression
bj-cbval2vv	|- ( A. x A. y ph <-> A. z A. w ps )

Distinct variable groups:   z, w, ph   x, y, ps   x, z, w, y

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

Proof of Theorem bj-cbval2vv

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ z ph
2		nfv 1843	. 2 |- F/ w ph
3		nfv 1843	. 2 |- F/ x ps
4		nfv 1843	. 2 |- F/ y ps
5		bj-cbval2vv.1	. 2 |- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
6	1, 2, 3, 4, 5	bj-cbval2v 32737	1 |- ( A. x A. y ph <-> A. z A. w ps )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   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

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

This theorem is referenced by: (None)