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Metamath Proof Explorer

Theorem ax5ea

Description: If a formula holds for some value of a variable not occurring in it, then it holds for all values of that variable. (Contributed by BJ, 28-Dec-2020)

		Ref	Expression
	Assertion	ax5ea	⊢ ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax5e	⊢ ( ∃ 𝑥 𝜑 → 𝜑 )
2		ax-5	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3	1 2	syl	⊢ ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜑 )