Theorem ax6o 977

Description: Show that the original axiom ax-6o 978 can be derived from ax-6 961 and others. See ax6 979 for the rederivation of ax-6 961 from ax-6o 978.

This theorem should not be referenced in any proof. Instead, use ax-6o 978 below so that uses of ax-6o 978 can be more easily identified.

Assertion

Ref	Expression
ax6o	|- (-. A.x -. A.xph -> ph)

Proof of Theorem ax6o

Step	Hyp	Ref	Expression
1		ax-4 973	. 2 |- (A.xph -> ph)
2		ax-6 961	. 2 |- (-. A.xph -> A.x -. A.xph)
3	1, 2	nsyl4 120	1 |- (-. A.x -. A.xph -> ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 954

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-6 961  ax-4 973

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