Theorem bj-3exbi 32600

Description: Closed form of 3exbii 1776. (Contributed by BJ, 6-May-2019.)

Assertion

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

Proof of Theorem bj-3exbi

Step	Hyp	Ref	Expression
1		exbi 1773	. . 3 |- ( A. z ( ph <-> ps ) -> ( E. z ph <-> E. z ps ) )
2	1	2alimi 1740	. 2 |- ( A. x A. y A. z ( ph <-> ps ) -> A. x A. y ( E. z ph <-> E. z ps ) )
3		bj-2exbi 32599	. 2 |- ( A. x A. y ( E. z ph <-> E. z ps ) -> ( E. x E. y E. z ph <-> E. x E. y E. z ps ) )
4	2, 3	syl 17	1 |- ( A. x A. y A. z ( ph <-> ps ) -> ( E. x E. y E. z ph <-> E. x E. y E. z ps ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)