Theorem degenmgmbas

Description: The base set of a degenerate magma. (Contributed by AV, 21-Aug-2026)

	Ref	Expression
Hypotheses	degenmgm.m	|- M = { <. ( Base ` ndx ) , { (/) , 1o } >. , <. ( +g ` ndx ) , { <. <. 1o , 1o >. , 1o >. , <. <. 1o , 2o >. , 1o >. , <. <. 1o , (/) >. , 1o >. } >. }
	degenmgmbas.b	|- B = ( Base ` M )
Assertion	degenmgmbas	|- B = { (/) , 1o }

Proof

Step	Hyp	Ref	Expression
1		degenmgm.m	|- M = { <. ( Base ` ndx ) , { (/) , 1o } >. , <. ( +g ` ndx ) , { <. <. 1o , 1o >. , 1o >. , <. <. 1o , 2o >. , 1o >. , <. <. 1o , (/) >. , 1o >. } >. }
2		degenmgmbas.b	|- B = ( Base ` M )
3		prex	|- { (/) , 1o } e. _V
4	1	grpbase	|- ( { (/) , 1o } e. _V -> { (/) , 1o } = ( Base ` M ) )
5	3 4	ax-mp	|- { (/) , 1o } = ( Base ` M )
6	2 5	eqtr4i	|- B = { (/) , 1o }