Theorem ax46 1015

Description: Proof of a single axiom that can replace ax-4 971 and ax-6o 976. See ax46to4 1016 and ax46to6 1017 for the re-derivation of those axioms. (Contributed by Scott Fenton, 12-Sep-2005.)

Assertion

Ref	Expression
ax46	|- ((A.x -. A.xph -> A.xph) -> ph)

Proof of Theorem ax46

Step	Hyp	Ref	Expression
1		ax-6o 976	. 2 |- (-. A.x -. A.xph -> ph)
2		ax-4 971	. 2 |- (A.xph -> ph)
3	1, 2	ja 137	1 |- ((A.x -. A.xph -> A.xph) -> ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 952

This theorem is referenced by:  ax46to4 1016  ax46to6 1017

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 971  ax-6o 976

Copyright terms: Public domain