Theorem exrot3 1620

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 1619	. 2 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )
2		excom 1594	. 2 |- ( E. z E. y E. x ph <-> E. y E. z E. x ph )
3	1, 2	bitri 182	1 |- ( E. x E. y E. z ph <-> E. y E. z E. x ph )

Syntax hints:   <-> wb 103   E.wex 1421

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-ial 1467

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  opabm  4035  rexiunxp  4496  dmoprab  5605  rnoprab  5607  cnvoprab  5875  xpassen  6327  dmaddpq  6569  dmmulpq  6570