Metamath Proof Explorer

Theorem nel0

Description: From the general negation of membership in A , infer that A is the empty set. (Contributed by BJ, 6-Oct-2018)

Ref Expression
Hypothesis nel0.1 ¬ x A
Assertion nel0 A =


Step Hyp Ref Expression
1 nel0.1 ¬ x A
2 eq0 A = x ¬ x A
3 2 1 mpgbir A =