Theorem excom13 1689

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 1664	. 2 |- ( E. x E. y E. z ph <-> E. y E. x E. z ph )
2		excom 1664	. . 3 |- ( E. x E. z ph <-> E. z E. x ph )
3	2	exbii 1605	. 2 |- ( E. y E. x E. z ph <-> E. y E. z E. x ph )
4		excom 1664	. 2 |- ( E. y E. z E. x ph <-> E. z E. y E. x ph )
5	1, 3, 4	3bitri 206	1 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )

Syntax hints:   <-> wb 105   E.wex 1492

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  exrot3  1690  exrot4  1691  euotd  4256