Theorem mndmgm

Description: A monoid is a magma. (Contributed by FL, 2-Nov-2009) (Revised by AV, 6-Jan-2020) (Proof shortened by AV, 6-Feb-2020)

	Ref	Expression
Assertion	mndmgm	⊢ ( 𝑀 ∈ Mnd → 𝑀 ∈ Mgm )

Proof

Step	Hyp	Ref	Expression
1		mndsgrp	⊢ ( 𝑀 ∈ Mnd → 𝑀 ∈ Smgrp )
2		sgrpmgm	⊢ ( 𝑀 ∈ Smgrp → 𝑀 ∈ Mgm )
3	1 2	syl	⊢ ( 𝑀 ∈ Mnd → 𝑀 ∈ Mgm )