Theorem bj-cmnssmndel

Description: Commutative monoids are monoids (elemental version). This is a more direct proof of cmnmnd , which relies on iscmn . (Contributed by BJ, 9-Jun-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-cmnssmndel	$$⊢A\in \mathrm{CMnd}\to A\in \mathrm{Mnd}$$

Proof

Step	Hyp	Ref	Expression
1		bj-cmnssmnd	$$⊢\mathrm{CMnd}\subseteq \mathrm{Mnd}$$
2	1	sseli	$$⊢A\in \mathrm{CMnd}\to A\in \mathrm{Mnd}$$