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Theorem axc5c4c711toc4 38121
Description: Rederivation of axc4 2126 from axc5c4c711 38119. 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 38119 . 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 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-11 2031  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by: (None)
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