Theorem ineqcomi

Description: Two ways of expressing that two classes have a given intersection. Inference form of ineqcom . Disjointness inference when C = (/) . (Contributed by Peter Mazsa, 26-Mar-2017) (Proof shortened by SN, 20-Sep-2024)

	Ref	Expression
Hypothesis	ineqcomi.1	|- ( A i^i B ) = C
Assertion	ineqcomi	|- ( B i^i A ) = C

Proof

Step	Hyp	Ref	Expression
1		ineqcomi.1	|- ( A i^i B ) = C
2		incom	|- ( B i^i A ) = ( A i^i B )
3	2 1	eqtri	|- ( B i^i A ) = C