Metamath Proof Explorer

Theorem eleenn

Description: If A is in ( EEN ) , then N is a natural. (Contributed by Scott Fenton, 1-Jul-2013)

Ref Expression
Assertion eleenn 
|- ( A e. ( EE ` N ) -> N e. NN )

Proof

Step Hyp Ref Expression
1 df-ee 
 |-  EE = ( n e. NN |-> ( RR ^m ( 1 ... n ) ) )
2 1 mptrcl 
 |-  ( A e. ( EE ` N ) -> N e. NN )