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 ∩ 𝐶 ) = ( 𝐵 ∩ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		ineq1i.1	⊢ 𝐴 = 𝐵
2		ineq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∩ 𝐶 ) = ( 𝐵 ∩ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ∩ 𝐶 ) = ( 𝐵 ∩ 𝐶 )