Theorem excom13 1100

Description: Swap 1st and 3rd existential quantifiers.

Assertion

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

Proof of Theorem excom13

Step	Hyp	Ref	Expression
1		excom 1048	. 2 |- (E.xE.yE.zph <-> E.yE.xE.zph)
2		excom 1048	. . 3 |- (E.xE.zph <-> E.zE.xph)
3	2	exbii 1053	. 2 |- (E.yE.xE.zph <-> E.yE.zE.xph)
4		excom 1048	. 2 |- (E.yE.zE.xph <-> E.zE.yE.xph)
5	1, 3, 4	3bitr 177	1 |- (E.xE.yE.zph <-> E.zE.yE.xph)

Syntax hints:   <-> wb 146  E.wex 982

This theorem is referenced by:  exrot3 1101  exrot4 1102

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-4 975  ax-5o 977  ax-6o 980

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983

Copyright terms: Public domain