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Metamath Proof Explorer

Theorem nfre1

Description: The setvar x is not free in E. x e. A ph . (Contributed by NM, 19-Mar-1997) (Revised by Mario Carneiro, 7-Oct-2016)

		Ref	Expression
	Assertion	nfre1	⊢ Ⅎ 𝑥 ∃ 𝑥 ∈ 𝐴 𝜑

Step	Hyp	Ref	Expression
1		df-rex	⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 ↔ ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) )
2		nfe1	⊢ Ⅎ 𝑥 ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜑 )
3	1 2	nfxfr	⊢ Ⅎ 𝑥 ∃ 𝑥 ∈ 𝐴 𝜑