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	|- ( |^| A " B ) C_ |^|_ x e. A ( x " B )

Proof

Step	Hyp	Ref	Expression
1		intimass	|- ( |^| A " B ) C_ |^| { y | E. x e. A y = ( x " B ) }
2		intima0	|- |^|_ x e. A ( x " B ) = |^| { y | E. x e. A y = ( x " B ) }
3	1 2	sseqtrri	|- ( |^| A " B ) C_ |^|_ x e. A ( x " B )