Theorem intimass2

Description: The image under the intersection of relations is a subset of the intersection of the images. (Contributed by RP, 13-Apr-2020)

	Ref	Expression
Assertion	intimass2	$$⊢\bigcap A\left[B\right]\subseteq \bigcap _{x\in A}x\left[B\right]$$

Proof

Step	Hyp	Ref	Expression
1		intimass	$$⊢\bigcap A\left[B\right]\subseteq \bigcap \left\{y|\exists x\in Ay=x\left[B\right]\right\}$$
2		intima0	$$⊢\bigcap _{x\in A}x\left[B\right]=\bigcap \left\{y|\exists x\in Ay=x\left[B\right]\right\}$$
3	1 2	sseqtrri	$$⊢\bigcap A\left[B\right]\subseteq \bigcap _{x\in A}x\left[B\right]$$