Definition df-sgrp2 45415

Description: A semigroup is a magma with an associative operation. Definition in section II.1 of [Bruck] p. 23, or of an "associative magma" in definition 5 of [BourbakiAlg1] p. 4, or of a semigroup in section 1.3 of [Hall] p. 7. (Contributed by AV, 6-Jan-2020.)

Assertion

Ref	Expression
df-sgrp2	⊢ SGrpALT = {𝑔 ∈ MgmALT ∣ (+g‘𝑔) assLaw (Base‘𝑔)}

Detailed syntax breakdown of Definition df-sgrp2

Step	Hyp	Ref	Expression
1		csgrp2 45411	. 2 class SGrpALT
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1538	. . . . 5 class 𝑔
4		cplusg 16962	. . . . 5 class +g
5	3, 4	cfv 6433	. . . 4 class (+g‘𝑔)
6		cbs 16912	. . . . 5 class Base
7	3, 6	cfv 6433	. . . 4 class (Base‘𝑔)
8		casslaw 45378	. . . 4 class assLaw
9	5, 7, 8	wbr 5074	. . 3 wff (+g‘𝑔) assLaw (Base‘𝑔)
10		cmgm2 45409	. . 3 class MgmALT
11	9, 2, 10	crab 3068	. 2 class {𝑔 ∈ MgmALT ∣ (+g‘𝑔) assLaw (Base‘𝑔)}
12	1, 11	wceq 1539	1 wff SGrpALT = {𝑔 ∈ MgmALT ∣ (+g‘𝑔) assLaw (Base‘𝑔)}

This definition is referenced by:  issgrpALT  45419