Theorem exrot4 1691

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 1689	. . 3 |- ( E. y E. z E. w ph <-> E. w E. z E. y ph )
2	1	exbii 1605	. 2 |- ( E. x E. y E. z E. w ph <-> E. x E. w E. z E. y ph )
3		excom13 1689	. 2 |- ( E. x E. w E. z E. y ph <-> E. z E. w E. x E. y ph )
4	2, 3	bitri 184	1 |- ( E. x E. y E. z E. w ph <-> E. z E. w E. x E. y ph )

Syntax hints:   <-> wb 105   E.wex 1492

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  ee8anv  1935  elvvv  4689  dfoprab2  5921  xpassen  6829  enq0sym  7430