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Metamath Proof Explorer

Theorem phicl

Description: Closure for the value of the Euler phi function. (Contributed by Mario Carneiro, 28-Feb-2014)

		Ref	Expression
	Assertion	phicl	$⊢ N \in ℕ \to ϕ (N) \in ℕ$

Step	Hyp	Ref	Expression
1		phicl2	$⊢ N \in ℕ \to ϕ (N) \in (1 \dots N)$
2		elfznn	$⊢ ϕ (N) \in (1 \dots N) \to ϕ (N) \in ℕ$
3	1 2	syl	$⊢ N \in ℕ \to ϕ (N) \in ℕ$