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 i^i B ) = C <-> ( B i^i A ) = C )

Proof

Step	Hyp	Ref	Expression
1		incom	|- ( A i^i B ) = ( B i^i A )
2	1	eqeq1i	|- ( ( A i^i B ) = C <-> ( B i^i A ) = C )