Theorem axc5c711toc5 39721

Description: Rederivation of ax-c5 39685 from axc5c711 39720. Only propositional calculus is used by the rederivation. (Contributed by NM, 19-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
axc5c711toc5	⊢ (∀𝑥𝜑 → 𝜑)

Proof of Theorem axc5c711toc5

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (∀𝑥𝜑 → (∀𝑥∀𝑥 ¬ ∀𝑥∀𝑥𝜑 → ∀𝑥𝜑))
2		axc5c711 39720	. 2 ⊢ ((∀𝑥∀𝑥 ¬ ∀𝑥∀𝑥𝜑 → ∀𝑥𝜑) → 𝜑)
3	1, 2	syl 18	1 ⊢ (∀𝑥𝜑 → 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-11 2191  ax-c5 39685  ax-c4 39686  ax-c7 39687

This theorem is used by: (None)