Theorem ax467to4 1020

Description: Re-derivation of ax-4 970 from ax467 1019. Only propositional calculus is used by the re-derivation.

Assertion

Ref	Expression
ax467to4	|- (A.xph -> ph)

Proof of Theorem ax467to4

Step	Hyp	Ref	Expression
1		ax-1 4	. 2 |- (A.xph -> (A.xA.x -. A.xA.xph -> A.xph))
2		ax467 1019	. 2 |- ((A.xA.x -. A.xA.xph -> A.xph) -> ph)
3	1, 2	syl 10	1 |- (A.xph -> ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 951

This theorem is referenced by:  ax467to6 1021

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-4 970  ax-5o 972  ax-6o 975

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