Theorem exrot3 1948

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 1947	. 2 |- ( E. x E. y E. z ph <-> E. z E. y E. x ph )
2		excom 1944	. 2 |- ( E. z E. y E. x ph <-> E. y E. z E. x ph )
3	1, 2	bitri 257	1 |- ( E. x E. y E. z ph <-> E. y E. z E. x ph )

Syntax hints:   <-> wb 189   E.wex 1671

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-11 1937

This theorem depends on definitions:  df-bi 190  df-ex 1672

This theorem is referenced by:  opabn0  4732  dmoprab  6396  rnoprab  6398  xpassen  7684  cnvoprab  28383  elima4  30492  brimg  30775  ellines  30990