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Metamath Proof Explorer

Theorem ringmnd

Description: A ring is a monoid under addition. (Contributed by Mario Carneiro, 7-Jan-2015)

Ref Expression
Assertion ringmnd ( 𝑅 ∈ Ring → 𝑅 ∈ Mnd )

Proof

Step Hyp Ref Expression
1 ringgrp ⊢ ( 𝑅 ∈ Ring → 𝑅 ∈ Grp )
2 1 grpmndd ⊢ ( 𝑅 ∈ Ring → 𝑅 ∈ Mnd )