Theorem ax67to7 1369

Description: Re-derivation of ax-7 1304 from ax67 1367. Note that ax-6o 1324 and ax-7 1304 are not used by the re-derivation.

Assertion

Ref	Expression
ax67to7	|- (A.xA.yph -> A.yA.xph)

Proof of Theorem ax67to7

Step	Hyp	Ref	Expression
1		ax67to6 1368	. . 3 |- (-. A.y -. A.y -. A.xA.yph -> -. A.xA.yph)
2	1	con4i 90	. 2 |- (A.xA.yph -> A.y -. A.y -. A.xA.yph)
3		ax67 1367	. . 3 |- (-. A.y -. A.xA.yph -> A.xph)
4	3	alimi 1338	. 2 |- (A.y -. A.y -. A.xA.yph -> A.yA.xph)
5	2, 4	syl 12	1 |- (A.xA.yph -> A.yA.xph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 1296

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-4 1319  ax-5o 1321  ax-6o 1324

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