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Metamath Proof Explorer

Theorem ablgrp

Description: An Abelian group is a group. (Contributed by NM, 26-Aug-2011)

Ref Expression
Assertion ablgrp ⊢ G ∈ Abel → G ∈ Grp

Proof

Step Hyp Ref Expression
1 isabl ⊢ G ∈ Abel ↔ G ∈ Grp ∧ G ∈ CMnd
2 1 simplbi ⊢ G ∈ Abel → G ∈ Grp