Theorem nnmcli

Description: _om is closed under multiplication. Inference form of nnmcl . (Contributed by Scott Fenton, 20-Apr-2012)

	Ref	Expression
Hypotheses	nncli.1	⊢ 𝐴 ∈ ω
	nncli.2	⊢ 𝐵 ∈ ω
Assertion	nnmcli	⊢ ( 𝐴 ·o 𝐵 ) ∈ ω

Proof

Step	Hyp	Ref	Expression
1		nncli.1	⊢ 𝐴 ∈ ω
2		nncli.2	⊢ 𝐵 ∈ ω
3		nnmcl	⊢ ( ( 𝐴 ∈ ω ∧ 𝐵 ∈ ω ) → ( 𝐴 ·o 𝐵 ) ∈ ω )
4	1 2 3	mp2an	⊢ ( 𝐴 ·o 𝐵 ) ∈ ω