Metamath Proof Explorer


Theorem exnel

Description: There is always a set not in y . (Contributed by Scott Fenton, 13-Dec-2010)

Ref Expression
Assertion exnel x¬xy

Proof

Step Hyp Ref Expression
1 elirrv ¬yy
2 1 nfth x¬yy
3 ax8 x=yxyyy
4 3 con3d x=y¬yy¬xy
5 2 4 spime ¬yyx¬xy
6 1 5 ax-mp x¬xy