This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem nfra1

Description: The setvar x is not free in A. x e. A ph . (Contributed by NM, 18-Oct-1996) (Revised by Mario Carneiro, 7-Oct-2016)

		Ref	Expression
	Assertion	nfra1	⊢ Ⅎ 𝑥 ∀ 𝑥 ∈ 𝐴 𝜑

Step	Hyp	Ref	Expression
1		df-ral	⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 ↔ ∀ 𝑥 ( 𝑥 ∈ 𝐴 → 𝜑 ) )
2		nfa1	⊢ Ⅎ 𝑥 ∀ 𝑥 ( 𝑥 ∈ 𝐴 → 𝜑 )
3	1 2	nfxfr	⊢ Ⅎ 𝑥 ∀ 𝑥 ∈ 𝐴 𝜑