Theorem axc5c711toc5 36670

Description: Rederivation of ax-c5 36634 from axc5c711 36669. 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 36669	. 2 ⊢ ((∀𝑥∀𝑥 ¬ ∀𝑥∀𝑥𝜑 → ∀𝑥𝜑) → 𝜑)
3	1, 2	syl 17	1 ⊢ (∀𝑥𝜑 → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-11 2158  ax-c5 36634  ax-c4 36635  ax-c7 36636

This theorem is referenced by: (None)