Theorem excom13 1667

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 1642	. 2 |- ( E. x E. y E. z ph <-> E. y E. x E. z ph )
2		excom 1642	. . 3 |- ( E. x E. z ph <-> E. z E. x ph )
3	2	exbii 1584	. 2 |- ( E. y E. x E. z ph <-> E. y E. z E. x ph )
4		excom 1642	. 2 |- ( E. y E. z E. x ph <-> E. z E. y E. x ph )
5	1, 3, 4	3bitri 205	1 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )

Syntax hints:   <-> wb 104   E.wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  exrot3  1668  exrot4  1669  euotd  4176