Theorem nfa1-o

Description: x is not free in A. x ph . (Contributed by Mario Carneiro, 11-Aug-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	nfa1-o	⊢ Ⅎ 𝑥 ∀ 𝑥 𝜑

Proof

Step	Hyp	Ref	Expression
1		hba1-o	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 ∀ 𝑥 𝜑 )
2	1	nf5i	⊢ Ⅎ 𝑥 ∀ 𝑥 𝜑