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Theorem ax467to6 2171
 Description: Re-derivation of ax-6o 2137 from ax467 2169. Note that ax-6o 2137 and ax-7 1734 are not used by the re-derivation. The use of alimi 1559 (which uses ax-4 2135) is allowed since we have already proved ax467to4 2170. (Contributed by NM, 19-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax467to6 x ¬ xφφ)

Proof of Theorem ax467to6
StepHypRef Expression
1 hba1-o 2149 . . . . . 6 (xφxxφ)
21con3i 127 . . . . 5 xxφ → ¬ xφ)
32alimi 1559 . . . 4 (x ¬ xxφx ¬ xφ)
43sps-o 2159 . . 3 (xx ¬ xxφx ¬ xφ)
54con3i 127 . 2 x ¬ xφ → ¬ xx ¬ xxφ)
6 pm2.21 100 . 2 xx ¬ xxφ → (xx ¬ xxφxφ))
7 ax467 2169 . 2 ((xx ¬ xxφxφ) → φ)
85, 6, 73syl 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-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-7 1734  ax-4 2135  ax-5o 2136  ax-6o 2137 This theorem is referenced by:  ax467to7  2172
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