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
|- F/_ x A
nfeq.2
|- F/_ x B
Assertion nfel
|- F/ x A e. B

Proof

Step Hyp Ref Expression
1 nfnfc.1
 |-  F/_ x A
2 nfeq.2
 |-  F/_ x B
3 1 a1i
 |-  ( T. -> F/_ x A )
4 2 a1i
 |-  ( T. -> F/_ x B )
5 3 4 nfeld
 |-  ( T. -> F/ x A e. B )
6 5 mptru
 |-  F/ x A e. B