Theorem ax67to7 2168

Description: Re-derivation of ax-7 1734 from ax67 2165. Note that ax-6o 2137 and ax-7 1734 are not used by the re-derivation. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem ax67to7

Step	Hyp	Ref	Expression
1		ax67to6 2167	. . 3 |- (-. A.y -. A.y -. A.xA.yph -> -. A.xA.yph)
2	1	con4i 122	. 2 |- (A.xA.yph -> A.y -. A.y -. A.xA.yph)
3		ax67 2165	. . 3 |- (-. A.y -. A.xA.yph -> A.xph)
4	3	alimi 1559	. 2 |- (A.y -. A.y -. A.xA.yph -> A.yA.xph)
5	2, 4	syl 15	1 |- (A.xA.yph -> A.yA.xph)

Syntax hints:  -. wn 3   -> wi 4  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-7 1734  ax-4 2135  ax-5o 2136  ax-6o 2137

This theorem is referenced by: (None)