Theorem 3exbii 1584

Description: Inference adding 3 existential quantifiers to both sides of an equivalence. (Contributed by NM, 2-May-1995.)

Hypothesis

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

Assertion

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

Proof of Theorem 3exbii

Step	Hyp	Ref	Expression
1		3exbii.1	. . 3 |- (ph <-> ps)
2	1	exbii 1582	. 2 |- (E.zph <-> E.zps)
3	2	2exbii 1583	1 |- (E.xE.yE.zph <-> E.xE.yE.zps)

Syntax hints:   <-> wb 176  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  eeeanv  1914  ceqsex6v  2900  oprabid  5551  dfoprab2  5559