Metamath Proof Explorer

Theorem sucexg

Description: The successor of a set is a set (generalization). (Contributed by NM, 5-Jun-1994)

Ref Expression
Assertion sucexg 
|- ( A e. V -> suc A e. _V )

Proof

Step Hyp Ref Expression
1 elex 
 |-  ( A e. V -> A e. _V )
2 sucexb 
 |-  ( A e. _V <-> suc A e. _V )
3 1 2 sylib 
 |-  ( A e. V -> suc A e. _V )