Theorem nfel

Description: Hypothesis builder for elementhood. (Contributed by NM, 1-Aug-1993) (Revised by Mario Carneiro, 11-Aug-2016) (Proof shortened by Wolf Lammen, 16-Nov-2019)

	Ref	Expression
Hypotheses	nfnfc.1	⊢ Ⅎ 𝑥 𝐴
	nfeq.2	⊢ Ⅎ 𝑥 𝐵
Assertion	nfel	⊢ Ⅎ 𝑥 𝐴 ∈ 𝐵

Proof

Step	Hyp	Ref	Expression
1		nfnfc.1	⊢ Ⅎ 𝑥 𝐴
2		nfeq.2	⊢ Ⅎ 𝑥 𝐵
3	1	a1i	⊢ ( ⊤ → Ⅎ 𝑥 𝐴 )
4	2	a1i	⊢ ( ⊤ → Ⅎ 𝑥 𝐵 )
5	3 4	nfeld	⊢ ( ⊤ → Ⅎ 𝑥 𝐴 ∈ 𝐵 )
6	5	mptru	⊢ Ⅎ 𝑥 𝐴 ∈ 𝐵