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Theorem axc5c4c711toc4 40943
Description: Rederivation of axc4 2342 from axc5c4c711 40941. Note that only propositional calculus is required for the rederivation. (Contributed by Andrew Salmon, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axc5c4c711toc4 (∀𝑥(∀𝑥𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))

Proof of Theorem axc5c4c711toc4
StepHypRef Expression
1 ax-1 6 . 2 (∀𝑥(∀𝑥𝜑𝜓) → (𝜑 → ∀𝑥(∀𝑥𝜑𝜓)))
2 ax-1 6 . 2 ((𝜑 → ∀𝑥(∀𝑥𝜑𝜓)) → (∀𝑥𝑥 ¬ ∀𝑥𝑥(∀𝑥𝜑𝜓) → (𝜑 → ∀𝑥(∀𝑥𝜑𝜓))))
3 axc5c4c711 40941 . 2 ((∀𝑥𝑥 ¬ ∀𝑥𝑥(∀𝑥𝜑𝜓) → (𝜑 → ∀𝑥(∀𝑥𝜑𝜓))) → (∀𝑥𝜑 → ∀𝑥𝜓))
41, 2, 33syl 18 1 (∀𝑥(∀𝑥𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-10 2146  ax-11 2162  ax-12 2179
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by: (None)
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