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 )

Proof

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 )