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Theorem ax67to7 2168
Description: Re-derivation of ax-7 1734 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
ax67to7 (xyφyxφ)

Proof of Theorem ax67to7
StepHypRef Expression
1 ax67to6 2167 . . 3 y ¬ y ¬ xyφ → ¬ xyφ)
21con4i 122 . 2 (xyφy ¬ y ¬ xyφ)
3 ax67 2165 . . 3 y ¬ xyφxφ)
43alimi 1559 . 2 (y ¬ y ¬ xyφyxφ)
52, 4syl 15 1 (xyφyxφ)
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: (None)
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