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Metamath Proof Explorer

Theorem axc5c7toc5

Description: Rederivation of ax-c5 from axc5c7 . Only propositional calculus is used for the rederivation. (Contributed by Scott Fenton, 12-Sep-2005) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	axc5c7toc5	⊢ ( ∀ 𝑥 𝜑 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax-1	⊢ ( ∀ 𝑥 𝜑 → ( ∀ 𝑥 ¬ ∀ 𝑥 𝜑 → ∀ 𝑥 𝜑 ) )
2		axc5c7	⊢ ( ( ∀ 𝑥 ¬ ∀ 𝑥 𝜑 → ∀ 𝑥 𝜑 ) → 𝜑 )
3	1 2	syl	⊢ ( ∀ 𝑥 𝜑 → 𝜑 )