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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 )