Theorem exrot3 1095

Description: Rotate existential quantifiers.

Assertion

Ref	Expression
exrot3	|- (E.xE.yE.zph <-> E.yE.zE.xph)

Proof of Theorem exrot3

Step	Hyp	Ref	Expression
1		excom13 1094	. 2 |- (E.xE.yE.zph <-> E.zE.yE.xph)
2		excom 1042	. 2 |- (E.zE.yE.xph <-> E.yE.zE.xph)
3	1, 2	bitr 173	1 |- (E.xE.yE.zph <-> E.yE.zE.xph)

Syntax hints:   <-> wb 146  E.wex 977

This theorem is referenced by:  opabn0 2813  dmoprab 3987  rnoprab 3989  xpassen 4421  genpn0 5078  genpass 5084

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-4 970  ax-5o 972  ax-6o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978

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