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Theorem axc711toc7 34520
Description: Rederivation of ax-c7 34489 from axc711 34518. Note that ax-c7 34489 and ax-11 2074 are not used by the rederivation. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axc711toc7 (¬ ∀𝑥 ¬ ∀𝑥𝜑𝜑)

Proof of Theorem axc711toc7
StepHypRef Expression
1 hba1-o 34501 . . . . 5 (∀𝑥𝜑 → ∀𝑥𝑥𝜑)
21con3i 150 . . . 4 (¬ ∀𝑥𝑥𝜑 → ¬ ∀𝑥𝜑)
32alimi 1779 . . 3 (∀𝑥 ¬ ∀𝑥𝑥𝜑 → ∀𝑥 ¬ ∀𝑥𝜑)
43con3i 150 . 2 (¬ ∀𝑥 ¬ ∀𝑥𝜑 → ¬ ∀𝑥 ¬ ∀𝑥𝑥𝜑)
5 axc711 34518 . 2 (¬ ∀𝑥 ¬ ∀𝑥𝑥𝜑 → ∀𝑥𝜑)
6 ax-c5 34487 . 2 (∀𝑥𝜑𝜑)
74, 5, 63syl 18 1 (¬ ∀𝑥 ¬ ∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-11 2074  ax-c5 34487  ax-c4 34488  ax-c7 34489
This theorem is referenced by:  axc711to11  34521
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