Theorem excom13 1579

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 1554	. 2 |- ( E. x E. y E. z ph <-> E. y E. x E. z ph )
2		excom 1554	. . 3 |- ( E. x E. z ph <-> E. z E. x ph )
3	2	exbii 1496	. 2 |- ( E. y E. x E. z ph <-> E. y E. z E. x ph )
4		excom 1554	. 2 |- ( E. y E. z E. x ph <-> E. z E. y E. x ph )
5	1, 3, 4	3bitri 195	1 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )

Syntax hints:   <-> wb 98   E.wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  exrot3  1580  exrot4  1581  euotd  3991