Theorem excom13 1743

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

Assertion

Ref	Expression
excom13	|- (E.xE.yE.zph <-> E.zE.yE.xph)

Proof of Theorem excom13

Step	Hyp	Ref	Expression
1		excom 1741	. 2 |- (E.xE.yE.zph <-> E.yE.xE.zph)
2		excom 1741	. . 3 |- (E.xE.zph <-> E.zE.xph)
3	2	exbii 1582	. 2 |- (E.yE.xE.zph <-> E.yE.zE.xph)
4		excom 1741	. 2 |- (E.yE.zE.xph <-> E.zE.yE.xph)
5	1, 3, 4	3bitri 262	1 |- (E.xE.yE.zph <-> E.zE.yE.xph)

Syntax hints:   <-> wb 176  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-7 1734

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  exrot3  1744  exrot4  1745