Metamath Proof Explorer


Theorem eq0

Description: A class is equal to the empty set if and only if it has no elements. Theorem 2 of Suppes p. 22. (Contributed by NM, 29-Aug-1993)

Ref Expression
Assertion eq0 A = x ¬ x A

Proof

Step Hyp Ref Expression
1 nfcv _ x A
2 1 eq0f A = x ¬ x A