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Metamath Proof Explorer

Theorem cntrss

Description: The center is a subset of the base field. (Contributed by Thierry Arnoux, 21-Aug-2023)

		Ref	Expression
	Hypothesis	cntrss.1	$⊢ B = {Base}_{M}$
	Assertion	cntrss	$⊢ Cntr (M) \subseteq B$

Step	Hyp	Ref	Expression
1		cntrss.1	$⊢ B = {Base}_{M}$
2		eqid	$⊢ Cntz (M) = Cntz (M)$
3	1 2	cntrval	$⊢ Cntz (M) (B) = Cntr (M)$
4	1 2	cntzssv	$⊢ Cntz (M) (B) \subseteq B$
5	3 4	eqsstrri	$⊢ Cntr (M) \subseteq B$