Metamath Proof Explorer


Theorem n0

Description: A class is nonempty if and only if it has at least one element. Proposition 5.17(1) of TakeutiZaring p. 20. (Contributed by NM, 29-Sep-2006)

Ref Expression
Assertion n0
|- ( A =/= (/) <-> E. x x e. A )

Proof

Step Hyp Ref Expression
1 nfcv
 |-  F/_ x A
2 1 n0f
 |-  ( A =/= (/) <-> E. x x e. A )