Theorem cbval2v 1798

Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 4-Feb-2005.)

Hypothesis

Ref	Expression
cbval2v.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )

Assertion

Ref	Expression
cbval2v	|- ( A. x A. y ph <-> A. z A. w ps )

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

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

Proof of Theorem cbval2v

Step	Hyp	Ref	Expression
1		nfv 1421	. 2 |- F/ z ph
2		nfv 1421	. 2 |- F/ w ph
3		nfv 1421	. 2 |- F/ x ps
4		nfv 1421	. 2 |- F/ y ps
5		cbval2v.1	. 2 |- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
6	1, 2, 3, 4, 5	cbval2 1796	1 |- ( A. x A. y ph <-> A. z A. w ps )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by: (None)