Theorem ineq12

Description: Equality theorem for intersection of two classes. (Contributed by NM, 8-May-1994)

	Ref	Expression
Assertion	ineq12	$$⊢\left(A=B\wedge C=D\right)\to A\cap C=B\cap D$$

Proof

Step	Hyp	Ref	Expression
1		ineq1	$$⊢A=B\to A\cap C=B\cap C$$
2		ineq2	$$⊢C=D\to B\cap C=B\cap D$$
3	1 2	sylan9eq	$$⊢\left(A=B\wedge C=D\right)\to A\cap C=B\cap D$$