Theorem ax6o 1018

Description: Show that the original axiom ax-6o 1019 can be derived from ax-6 1002 and others. See ax6 1020 for the rederivation of ax-6 1002 from ax-6o 1019.

This theorem should not be referenced in any proof. Instead, use ax-6o 1019 below so that uses of ax-6o 1019 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 1014	. 2 |- (A.xph -> ph)
2		ax-6 1002	. 2 |- (-. A.xph -> A.x -. A.xph)
3	1, 2	nsyl4 126	1 |- (-. A.x -. A.xph -> ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 995

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-6 1002  ax-4 1014

Copyright terms: Public domain