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Theorem ax67to6 2167
Description: Re-derivation of ax-6o 2137 from ax67 2165. Note that ax-6o 2137 and ax-7 1734 are not used by the re-derivation. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax67to6 x ¬ xφφ)

Proof of Theorem ax67to6
StepHypRef Expression
1 hba1-o 2149 . . . . 5 (xφxxφ)
21con3i 127 . . . 4 xxφ → ¬ xφ)
32alimi 1559 . . 3 (x ¬ xxφx ¬ xφ)
43con3i 127 . 2 x ¬ xφ → ¬ x ¬ xxφ)
5 ax67 2165 . 2 x ¬ xxφxφ)
6 ax-4 2135 . 2 (xφφ)
74, 5, 63syl 18 1 x ¬ xφφ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-7 1734  ax-4 2135  ax-5o 2136  ax-6o 2137
This theorem is referenced by:  ax67to7  2168
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