Theorem phicld

Description: Closure for the value of the Euler phi function. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	phicld.1	|- ( ph -> N e. NN )
Assertion	phicld	|- ( ph -> ( phi ` N ) e. NN )

Proof

Step	Hyp	Ref	Expression
1		phicld.1	|- ( ph -> N e. NN )
2		phicl	|- ( N e. NN -> ( phi ` N ) e. NN )
3	1 2	syl	|- ( ph -> ( phi ` N ) e. NN )