Theorem exrot3 1668

Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.)

Assertion

Ref	Expression
exrot3	|- ( E. x E. y E. z ph <-> E. y E. z E. x ph )

Proof of Theorem exrot3

Step	Hyp	Ref	Expression
1		excom13 1667	. 2 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )
2		excom 1642	. 2 |- ( E. z E. y E. x ph <-> E. y E. z E. x ph )
3	1, 2	bitri 183	1 |- ( E. x E. y E. z ph <-> E. y E. z E. x ph )

Syntax hints:   <-> wb 104   E.wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  opabm  4202  rexiunxp  4681  dmoprab  5852  rnoprab  5854  cnvoprab  6131  xpassen  6724  dmaddpq  7187  dmmulpq  7188