Theorem ineqcomi

Description: Disjointness inference (when C = (/) ), inference form of ineqcom . (Contributed by Peter Mazsa, 26-Mar-2017)

	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		ineqcom	$$⊢A\cap B=C\leftrightarrow B\cap A=C$$
3	1 2	mpbi	$$⊢B\cap A=C$$