Theorem intima0

Description: Two ways of expressing the intersection of images of a class. (Contributed by RP, 13-Apr-2020)

	Ref	Expression
Assertion	intima0	$$⊢\bigcap _{a\in A}a\left[B\right]=\bigcap \left\{x|\exists a\in Ax=a\left[B\right]\right\}$$

Proof

Step	Hyp	Ref	Expression
1		vex	$$⊢a\in \mathrm{V}$$
2	1	imaex	$$⊢a\left[B\right]\in \mathrm{V}$$
3	2	dfiin2	$$⊢\bigcap _{a\in A}a\left[B\right]=\bigcap \left\{x|\exists a\in Ax=a\left[B\right]\right\}$$