Theorem exrot3 1801

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 1800	. 2 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )
2		excom 1798	. 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 1596

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-11 1791

This theorem depends on definitions:  df-bi 185  df-ex 1597

This theorem is referenced by:  opabn0  4783  dmoprab  6377  rnoprab  6379  xpassen  7621  elima4  29104  brimg  29482  ellines  29697