Theorem inteqd

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

	Ref	Expression
Hypothesis	inteqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	inteqd	⊢ ( 𝜑 → ∩ 𝐴 = ∩ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		inteqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		inteq	⊢ ( 𝐴 = 𝐵 → ∩ 𝐴 = ∩ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → ∩ 𝐴 = ∩ 𝐵 )