Theorem 3exbii 1541

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

Hypothesis

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

Assertion

Ref	Expression
3exbii	|- ( E. x E. y E. z ph <-> E. x E. y E. z ps )

Proof of Theorem 3exbii

Step	Hyp	Ref	Expression
1		exbii.1	. . 3 |- ( ph <-> ps )
2	1	exbii 1539	. 2 |- ( E. z ph <-> E. z ps )
3	2	2exbii 1540	1 |- ( E. x E. y E. z ph <-> E. x E. y E. z ps )

Syntax hints:   <-> wb 103   E.wex 1424

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-ial 1470

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  eeeanv  1853  ceqsex6v  2656  oprabid  5619  dfoprab2  5634  dftpos3  5962  xpassen  6479