Theorem bi3ex 735

Description: Inference adding 3 existential quantifiers to both sides of an equivalence.

Hypothesis

Ref	Expression
bi3ex.1	|- (ph <-> ps)

Assertion

Ref	Expression
bi3ex	|- (E.xE.yE.zph <-> E.xE.yE.zps)

Proof of Theorem bi3ex

Step	Hyp	Ref	Expression
1		bi3ex.1	. . 3 |- (ph <-> ps)
2	1	biex 733	. 2 |- (E.zph <-> E.zps)
3	2	bi2ex 734	1 |- (E.xE.yE.zph <-> E.xE.yE.zps)

Syntax hints:   <-> wb 127  E.wex 678

This theorem is referenced by:  eeeanv 981  dfoprab2 3021  xpassen 3344  distrlem1pr 3921

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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