Theorem ressbasss2

Description: The base set of a restriction to A is a subset of A . (Contributed by SN, 10-Jan-2025)

	Ref	Expression
Hypothesis	ressbasss2.r	$$⊢R=W{\upharpoonright }_{𝑠}A$$
Assertion	ressbasss2	$$⊢{\mathrm{Base}}_R\subseteq A$$

Proof

Step	Hyp	Ref	Expression
1		ressbasss2.r	$$⊢R=W{\upharpoonright }_{𝑠}A$$
2		eqid	$$⊢{\mathrm{Base}}_W={\mathrm{Base}}_W$$
3	1 2	ressbasssg	$$⊢{\mathrm{Base}}_R\subseteq A\cap {\mathrm{Base}}_W$$
4		inss1	$$⊢A\cap {\mathrm{Base}}_W\subseteq A$$
5	3 4	sstri	$$⊢{\mathrm{Base}}_R\subseteq A$$