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		grpmnd	⊢ ( 𝑅 ∈ Grp → 𝑅 ∈ Mnd )
3	1 2	syl	⊢ ( 𝑅 ∈ Ring → 𝑅 ∈ Mnd )