Theorem ineq1i

Description: Equality inference for intersection of two classes. (Contributed by NM, 26-Dec-1993)

	Ref	Expression
Hypothesis	ineq1i.1	$$⊢A=B$$
Assertion	ineq1i	$$⊢A\cap C=B\cap C$$

Proof

Step	Hyp	Ref	Expression
1		ineq1i.1	$$⊢A=B$$
2		ineq1	$$⊢A=B\to A\cap C=B\cap C$$
3	1 2	ax-mp	$$⊢A\cap C=B\cap C$$