Theorem reldmxpc

Description: The binary product of categories is a proper operator, so it can be used with ovprc1 , elbasov , strov2rcl , and so on. See reldmxpcALT for an alternate proof with less "essential steps" but more "bytes". (Proposed by SN, 15-Oct-2025.) (Contributed by Zhi Wang, 15-Oct-2025)

	Ref	Expression
Assertion	reldmxpc	|- Rel dom Xc.

Proof

Step	Hyp	Ref	Expression
1		relxp	|- Rel ( _V X. _V )
2		fnxpc	|- Xc. Fn ( _V X. _V )
3	2	fndmi	|- dom Xc. = ( _V X. _V )
4	3	releqi	|- ( Rel dom Xc. <-> Rel ( _V X. _V ) )
5	1 4	mpbir	|- Rel dom Xc.