Theorem excom13 2044

Description: Swap 1st and 3rd existential quantifiers. (Contributed by NM, 9-Mar-1995.)

Assertion

Ref	Expression
excom13	|- ( E. x E. y E. z ph <-> E. z E. y E. x ph )

Proof of Theorem excom13

Step	Hyp	Ref	Expression
1		excom 2042	. 2 |- ( E. x E. y E. z ph <-> E. y E. x E. z ph )
2		excom 2042	. . 3 |- ( E. x E. z ph <-> E. z E. x ph )
3	2	exbii 1774	. 2 |- ( E. y E. x E. z ph <-> E. y E. z E. x ph )
4		excom 2042	. 2 |- ( E. y E. z E. x ph <-> E. z E. y E. x ph )
5	1, 3, 4	3bitri 286	1 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )

Syntax hints:   <-> wb 196   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  ax-11 2034

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

This theorem is referenced by:  exrot3  2045  exrot4  2046  euotd  4975  elfuns  32022