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Theorem axc5c4c711toc4 39573
 Description: Rederivation of axc4 2296 from axc5c4c711 39571. 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 39571 . 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 1599 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-10 2135  ax-11 2150  ax-12 2163 This theorem depends on definitions:  df-bi 199  df-ex 1824 This theorem is referenced by: (None)
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