Theorem resss

Description: A class includes its restriction. Exercise 15 of TakeutiZaring p. 25. (Contributed by NM, 2-Aug-1994)

	Ref	Expression
Assertion	resss	$$⊢{A\upharpoonright }_B\subseteq A$$

Proof

Step	Hyp	Ref	Expression
1		df-res	$$⊢{A\upharpoonright }_B=A\cap \left(B\times \mathrm{V}\right)$$
2		inss1	$$⊢A\cap \left(B\times \mathrm{V}\right)\subseteq A$$
3	1 2	eqsstri	$$⊢{A\upharpoonright }_B\subseteq A$$