Theorem axc5c7toc7 36043

Description: Rederivation of ax-c7 36015 from axc5c7 36041. Only propositional calculus is used for the rederivation. (Contributed by Scott Fenton, 12-Sep-2005.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
axc5c7toc7	⊢ (¬ ∀𝑥 ¬ ∀𝑥𝜑 → 𝜑)

Proof of Theorem axc5c7toc7

Step	Hyp	Ref	Expression
1		pm2.21 123	. 2 ⊢ (¬ ∀𝑥 ¬ ∀𝑥𝜑 → (∀𝑥 ¬ ∀𝑥𝜑 → ∀𝑥𝜑))
2		axc5c7 36041	. 2 ⊢ ((∀𝑥 ¬ ∀𝑥𝜑 → ∀𝑥𝜑) → 𝜑)
3	1, 2	syl 17	1 ⊢ (¬ ∀𝑥 ¬ ∀𝑥𝜑 → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1531

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-c5 36013  ax-c7 36015

This theorem is referenced by: (None)