Theorem axc5c7toc5 38854

Description: Rederivation of ax-c5 38825 from axc5c7 38853. 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
axc5c7toc5	⊢ (∀𝑥𝜑 → 𝜑)

Proof of Theorem axc5c7toc5

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (∀𝑥𝜑 → (∀𝑥 ¬ ∀𝑥𝜑 → ∀𝑥𝜑))
2		axc5c7 38853	. 2 ⊢ ((∀𝑥 ¬ ∀𝑥𝜑 → ∀𝑥𝜑) → 𝜑)
3	1, 2	syl 17	1 ⊢ (∀𝑥𝜑 → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1537

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-c5 38825  ax-c7 38827

This theorem is referenced by: (None)