Theorem cbvex2v 1314

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-17 968	. 2 |- (ph -> A.zph)
2		ax-17 968	. 2 |- (ph -> A.wph)
3		ax-17 968	. 2 |- (ps -> A.xps)
4		ax-17 968	. 2 |- (ps -> A.yps)
5		cbval2v.1	. 2 |- ((x = z /\ y = w) -> (ph <-> ps))
6	1, 2, 3, 4, 5	cbvex2 1312	1 |- (E.xE.yph <-> E.zE.wps)

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223   = wceq 953  E.wex 977

This theorem is referenced by:  cbvex4v 1317  2mo 1440  2eu6 1447  th3qlem1 4298  genpv 5074

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978

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