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Theorem axc5c7toc5 33015
Description: Rederivation of ax-c5 32986 from axc5c7 33014. Only propositional calculus is used for the rederivation. (Contributed by Scott Fenton, 12-Sep-2005.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axc5c7toc5 (∀𝑥𝜑𝜑)

Proof of Theorem axc5c7toc5
StepHypRef Expression
1 ax-1 6 . 2 (∀𝑥𝜑 → (∀𝑥 ¬ ∀𝑥𝜑 → ∀𝑥𝜑))
2 axc5c7 33014 . 2 ((∀𝑥 ¬ ∀𝑥𝜑 → ∀𝑥𝜑) → 𝜑)
31, 2syl 17 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-c5 32986  ax-c7 32988
This theorem is referenced by: (None)
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