Theorem ineqcom

Description: Two ways of expressing that two classes have a given intersection. This is often used when that given intersection is the empty set, in which case the statement displays two ways of expressing that two classes are disjoint (when C = (/) : ( ( A i^i B ) = (/) <-> ( B i^i A ) = (/) ) ). (Contributed by Peter Mazsa, 22-Mar-2017)

	Ref	Expression
Assertion	ineqcom	$$⊢A\cap B=C\leftrightarrow B\cap A=C$$

Proof

Step	Hyp	Ref	Expression
1		incom	$$⊢A\cap B=B\cap A$$
2	1	eqeq1i	$$⊢A\cap B=C\leftrightarrow B\cap A=C$$