Theorem exrot4 1581

Description: Rotate existential quantifiers twice. (Contributed by NM, 9-Mar-1995.)

Assertion

Ref	Expression
exrot4	|- ( E. x E. y E. z E. w ph <-> E. z E. w E. x E. y ph )

Proof of Theorem exrot4

Step	Hyp	Ref	Expression
1		excom13 1579	. . 3 |- ( E. y E. z E. w ph <-> E. w E. z E. y ph )
2	1	exbii 1496	. 2 |- ( E. x E. y E. z E. w ph <-> E. x E. w E. z E. y ph )
3		excom13 1579	. 2 |- ( E. x E. w E. z E. y ph <-> E. z E. w E. x E. y ph )
4	2, 3	bitri 173	1 |- ( E. x E. y E. z E. w ph <-> E. z E. w E. x E. y ph )

Syntax hints:   <-> wb 98   E.wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  ee8anv  1810  elvvv  4403  dfoprab2  5552  xpassen  6304  enq0sym  6530