Theorem dicdmN

Description: Domain of the partial isomorphism C. (Contributed by NM, 8-Mar-2014) (New usage is discouraged.)

	Ref	Expression
Hypotheses	dicfn.l	|- .<_ = ( le ` K )
	dicfn.a	|- A = ( Atoms ` K )
	dicfn.h	|- H = ( LHyp ` K )
	dicfn.i	|- I = ( ( DIsoC ` K ) ` W )
Assertion	dicdmN	|- ( ( K e. V /\ W e. H ) -> dom I = { p e. A | -. p .<_ W } )

Proof

Step	Hyp	Ref	Expression
1		dicfn.l	|- .<_ = ( le ` K )
2		dicfn.a	|- A = ( Atoms ` K )
3		dicfn.h	|- H = ( LHyp ` K )
4		dicfn.i	|- I = ( ( DIsoC ` K ) ` W )
5	1 2 3 4	dicfnN	|- ( ( K e. V /\ W e. H ) -> I Fn { p e. A | -. p .<_ W } )
6	5	fndmd	|- ( ( K e. V /\ W e. H ) -> dom I = { p e. A | -. p .<_ W } )