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Metamath Proof Explorer

Theorem axc5c711toc5

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

		Ref	Expression
	Assertion	axc5c711toc5	⊢ ( ∀ 𝑥 𝜑 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax-1	⊢ ( ∀ 𝑥 𝜑 → ( ∀ 𝑥 ∀ 𝑥 ¬ ∀ 𝑥 ∀ 𝑥 𝜑 → ∀ 𝑥 𝜑 ) )
2		axc5c711	⊢ ( ( ∀ 𝑥 ∀ 𝑥 ¬ ∀ 𝑥 ∀ 𝑥 𝜑 → ∀ 𝑥 𝜑 ) → 𝜑 )
3	1 2	syl	⊢ ( ∀ 𝑥 𝜑 → 𝜑 )