Theorem inteqd

Description: Equality deduction for class intersection. (Contributed by NM, 2-Sep-2003)

	Ref	Expression
Hypothesis	inteqd.1	$$⊢\phi \to A=B$$
Assertion	inteqd	$$⊢\phi \to \bigcap A=\bigcap B$$

Proof

Step	Hyp	Ref	Expression
1		inteqd.1	$$⊢\phi \to A=B$$
2		inteq	$$⊢A=B\to \bigcap A=\bigcap B$$
3	1 2	syl	$$⊢\phi \to \bigcap A=\bigcap B$$