Metamath Proof Explorer


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 )