Theorem ax67to6 1023

Description: Re-derivation of ax-6o 980 from ax67 1022. Note that ax-6o 980 and ax-7 964 are not used by the re-derivation.

Assertion

Ref	Expression
ax67to6	|- (-. A.x -. A.xph -> ph)

Proof of Theorem ax67to6

Step	Hyp	Ref	Expression
1		hba1 1005	. . . . 5 |- (A.xph -> A.xA.xph)
2	1	con3i 98	. . . 4 |- (-. A.xA.xph -> -. A.xph)
3	2	19.20i 994	. . 3 |- (A.x -. A.xA.xph -> A.x -. A.xph)
4	3	con3i 98	. 2 |- (-. A.x -. A.xph -> -. A.x -. A.xA.xph)
5		ax67 1022	. 2 |- (-. A.x -. A.xA.xph -> A.xph)
6		ax-4 975	. 2 |- (A.xph -> ph)
7	4, 5, 6	3syl 20	1 |- (-. A.x -. A.xph -> ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 956

This theorem is referenced by:  ax67to7 1024

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-4 975  ax-5o 977  ax-6o 980

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