Theorem excomim 727

Description: One direction of Theorem 19.11 of [Margaris] p. 89.

Assertion

Ref	Expression
excomim	|- (E.xE.yph -> E.yE.xph)

Proof of Theorem excomim

Step	Hyp	Ref	Expression
1		19.8a 712	. . . 4 |- (ph -> E.xph)
2	1	19.22i 723	. . 3 |- (E.yph -> E.yE.xph)
3	2	19.22i 723	. 2 |- (E.xE.yph -> E.xE.yE.xph)
4		hbe1 709	. . . 4 |- (E.xph -> A.xE.xph)
5	4	hbex 701	. . 3 |- (E.yE.xph -> A.xE.yE.xph)
6	5	19.9r 718	. 2 |- (E.yE.xph <-> E.xE.yE.xph)
7	3, 6	sylibr 175	1 |- (E.xE.yph -> E.yE.xph)

Syntax hints:   -> wi 2  E.wex 678

This theorem is referenced by:  excom 728  2euswap 1065  prnmadd 3894

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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