Metamath Proof Explorer

Theorem mndomgmid

Description: A monoid is a magma with an identity element. (Contributed by FL, 18-Feb-2010) (New usage is discouraged.)

		Ref	Expression
	Assertion	mndomgmid	$⊢ G \in MndOp \to G \in (Magma \cap ExId)$

Step	Hyp	Ref	Expression
1		mndoismgmOLD	$⊢ G \in MndOp \to G \in Magma$
2		mndoisexid	$⊢ G \in MndOp \to G \in ExId$
3	1 2	elind	$⊢ G \in MndOp \to G \in (Magma \cap ExId)$