Theorem excomim 1553

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 1482	. . 3 |- ( ph -> E. x ph )
2	1	2eximi 1492	. 2 |- ( E. x E. y ph -> E. x E. y E. x ph )
3		hbe1 1384	. . . 4 |- ( E. x ph -> A. x E. x ph )
4	3	hbex 1527	. . 3 |- ( E. y E. x ph -> A. x E. y E. x ph )
5	4	19.9h 1534	. 2 |- ( E. x E. y E. x ph <-> E. y E. x ph )
6	2, 5	sylib 127	1 |- ( E. x E. y ph -> E. y E. x ph )

Syntax hints:   -> wi 4   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:  excom  1554  2euswapdc  1991