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