Theorem exrot3 1701

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 1700	. 2 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )
2		excom 1675	. 2 |- ( E. z E. y E. x ph <-> E. y E. z E. x ph )
3	1, 2	bitri 184	1 |- ( E. x E. y E. z ph <-> E. y E. z E. x ph )

Syntax hints:   <-> wb 105   E.wex 1503

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  opabm  4298  rexiunxp  4787  dmoprab  5977  rnoprab  5979  cnvoprab  6259  xpassen  6856  dmaddpq  7408  dmmulpq  7409