Metamath Proof Explorer

Theorem mndoissmgrpOLD

Description: Obsolete version of mndsgrp as of 3-Feb-2020. A monoid is a semigroup. (Contributed by FL, 2-Nov-2009) (New usage is discouraged.) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	mndoissmgrpOLD	$⊢ G \in MndOp \to G \in SemiGrp$

Proof

Step	Hyp	Ref	Expression
1		elin	$⊢ G \in (SemiGrp \cap ExId) \leftrightarrow (G \in SemiGrp \land G \in ExId)$
2	1	simplbi	$⊢ G \in (SemiGrp \cap ExId) \to G \in SemiGrp$
3		df-mndo	$⊢ MndOp = SemiGrp \cap ExId$
4	2 3	eleq2s	$⊢ G \in MndOp \to G \in SemiGrp$