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