Metamath Proof Explorer


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 _ x A
nfeq.2 _ x B
Assertion nfel x A B

Proof

Step Hyp Ref Expression
1 nfnfc.1 _ x A
2 nfeq.2 _ x B
3 1 a1i _ x A
4 2 a1i _ x B
5 3 4 nfeld x A B
6 5 mptru x A B