Theorem excomim 1641

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 1569	. . 3 |- ( ph -> E. x ph )
2	1	2eximi 1580	. 2 |- ( E. x E. y ph -> E. x E. y E. x ph )
3		hbe1 1471	. . . 4 |- ( E. x ph -> A. x E. x ph )
4	3	hbex 1615	. . 3 |- ( E. y E. x ph -> A. x E. y E. x ph )
5	4	19.9h 1622	. 2 |- ( E. x E. y E. x ph <-> E. y E. x ph )
6	2, 5	sylib 121	1 |- ( E. x E. y ph -> E. y E. x ph )

Syntax hints:   -> wi 4   E.wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  excom  1642  2euswapdc  2090