Theorem cbvex2v 1317

Description: Rule used to change bound variables with implicit substitution.

Hypothesis

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

Assertion

Ref	Expression
cbvex2v	|- (E.xE.yph <-> E.zE.wps)

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

Proof of Theorem cbvex2v

Step	Hyp	Ref	Expression
1		ax-17 969	. 2 |- (ph -> A.zph)
2		ax-17 969	. 2 |- (ph -> A.wph)
3		ax-17 969	. 2 |- (ps -> A.xps)
4		ax-17 969	. 2 |- (ps -> A.yps)
5		cbval2v.1	. 2 |- ((x = z /\ y = w) -> (ph <-> ps))
6	1, 2, 3, 4, 5	cbvex2 1315	1 |- (E.xE.yph <-> E.zE.wps)

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223   = wceq 954  E.wex 978

This theorem is referenced by:  cbvex4v 1320  2mo 1445  2eu6 1452  th3qlem1 4304  genpv 5082

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979

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