Metamath Proof Explorer


Theorem ablgrpd

Description: An Abelian group is a group, deduction form of ablgrp . (Contributed by Rohan Ridenour, 3-Aug-2023)

Ref Expression
Hypothesis ablgrpd.1
|- ( ph -> G e. Abel )
Assertion ablgrpd
|- ( ph -> G e. Grp )

Proof

Step Hyp Ref Expression
1 ablgrpd.1
 |-  ( ph -> G e. Abel )
2 ablgrp
 |-  ( G e. Abel -> G e. Grp )
3 1 2 syl
 |-  ( ph -> G e. Grp )