Theorem exrot3 1860

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 1859	. 2 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )
2		excom 1857	. 2 |- ( E. z E. y E. x ph <-> E. y E. z E. x ph )
3	1, 2	bitri 249	1 |- ( E. x E. y E. z ph <-> E. y E. z E. x ph )

Syntax hints:   <-> wb 184   E.wex 1620

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-11 1850

This theorem depends on definitions:  df-bi 185  df-ex 1621

This theorem is referenced by:  opabn0  4692  dmoprab  6282  rnoprab  6284  xpassen  7530  cnvoprab  27696  elima4  29374  brimg  29740  ellines  29955