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Metamath Proof Explorer

Theorem nfia1

Description: Lemma 23 of Monk2 p. 114. (Contributed by Mario Carneiro, 24-Sep-2016)

		Ref	Expression
	Assertion	nfia1	⊢ Ⅎ 𝑥 ( ∀ 𝑥 𝜑 → ∀ 𝑥 𝜓 )

Step	Hyp	Ref	Expression
1		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 𝜑
2		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 𝜓
3	1 2	nfim	⊢ Ⅎ 𝑥 ( ∀ 𝑥 𝜑 → ∀ 𝑥 𝜓 )