Theorem ax67to7 996

Description: Re-derivation of ax-7 954 from ax67 994. Note that ax-6 953 and ax-7 954 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 995	. . 3 |- (-. A.y -. A.y -. A.xA.yph -> -. A.xA.yph)
2	1	a3i 74	. 2 |- (A.xA.yph -> A.y -. A.y -. A.xA.yph)
3		ax67 994	. . 3 |- (-. A.y -. A.xA.yph -> A.xph)
4	3	19.20i 968	. 2 |- (A.y -. A.y -. A.xA.yph -> A.yA.xph)
5	2, 4	syl 10	1 |- (A.xA.yph -> A.yA.xph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 950

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-7 954  ax-gen 955

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