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	$$⊢A\cap B=C$$
Assertion	ineqcomi	$$⊢B\cap A=C$$

Proof

Step	Hyp	Ref	Expression
1		ineqcomi.1	$$⊢A\cap B=C$$
2		incom	$$⊢B\cap A=A\cap B$$
3	2 1	eqtri	$$⊢B\cap A=C$$