Theorem excomim 1045

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 1029	. . 3 |- (ph -> E.xph)
2	1	19.22i2 1041	. 2 |- (E.xE.yph -> E.xE.yE.xph)
3		hbe1 1016	. . . 4 |- (E.xph -> A.xE.xph)
4	3	hbex 1006	. . 3 |- (E.yE.xph -> A.xE.yE.xph)
5	4	19.9 1036	. 2 |- (E.xE.yE.xph <-> E.yE.xph)
6	2, 5	sylib 198	1 |- (E.xE.yph -> E.yE.xph)

Syntax hints:   -> wi 3  E.wex 980

This theorem is referenced by:  excom 1046  2euswap 1445  prnmadd 5100

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-4 973  ax-5o 975  ax-6o 978

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

Copyright terms: Public domain