Theorem 3exbi 1053

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

Hypothesis

Ref	Expression
3exbii.1	|- (ph <-> ps)

Assertion

Ref	Expression
3exbi	|- (E.xE.yE.zph <-> E.xE.yE.zps)

Proof of Theorem 3exbi

Step	Hyp	Ref	Expression
1		3exbii.1	. . 3 |- (ph <-> ps)
2	1	exbii 1051	. 2 |- (E.zph <-> E.zps)
3	2	2exbii 1052	1 |- (E.xE.yE.zph <-> E.xE.yE.zps)

Syntax hints:   <-> wb 146  E.wex 980

This theorem is referenced by:  eeeanv 1324  dfoprab2 3991  xpassen 4441  distrlem1pr 5127  eeeeanv 10436  isalg 10653  algi 10660

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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