Theorem 3exbii 1641

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. x E. y E. z ph <-> E. x E. y E. z ps )

Proof of Theorem 3exbii

Step	Hyp	Ref	Expression
1		3exbii.1	. . 3 |- ( ph <-> ps )
2	1	exbii 1639	. 2 |- ( E. z ph <-> E. z ps )
3	2	2exbii 1640	1 |- ( E. x E. y E. z ph <-> E. x E. y E. z ps )

Syntax hints:   <-> wb 184   E.wex 1591

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607

This theorem depends on definitions:  df-bi 185  df-ex 1592

This theorem is referenced by:  4exdistr  1948  ceqsex6v  3148  oprabid  6299  dfoprab2  6318  dftpos3  6963  xpassen  7601  ellines  29365  bnj916  32945  bnj917  32946  bnj983  32963  bnj996  32967  bnj1021  32976  bnj1033  32979