Theorem ineq1d

Description: Equality deduction for intersection of two classes. (Contributed by NM, 10-Apr-1994)

	Ref	Expression
Hypothesis	ineq1d.1	$$⊢\phi \to A=B$$
Assertion	ineq1d	$$⊢\phi \to A\cap C=B\cap C$$

Proof

Step	Hyp	Ref	Expression
1		ineq1d.1	$$⊢\phi \to A=B$$
2		ineq1	$$⊢A=B\to A\cap C=B\cap C$$
3	1 2	syl	$$⊢\phi \to A\cap C=B\cap C$$