Theorem excomim 1709

Description: One direction of Theorem 19.11 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
excomim	|- ( E. x E. y ph -> E. y E. x ph )

Proof of Theorem excomim

Step	Hyp	Ref	Expression
1		19.8a 1636	. . 3 |- ( ph -> E. x ph )
2	1	2eximi 1647	. 2 |- ( E. x E. y ph -> E. x E. y E. x ph )
3		hbe1 1541	. . . 4 |- ( E. x ph -> A. x E. x ph )
4	3	hbex 1682	. . 3 |- ( E. y E. x ph -> A. x E. y E. x ph )
5	4	19.9h 1689	. 2 |- ( E. x E. y E. x ph <-> E. y E. x ph )
6	2, 5	sylib 122	1 |- ( E. x E. y ph -> E. y E. x ph )

Syntax hints:   -> wi 4   E.wex 1538

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-ial 1580

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  excom  1710  2euswapdc  2169