Theorem dibdmN

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

	Ref	Expression
Hypotheses	dibfn.b	|- B = ( Base ` K )
	dibfn.l	|- .<_ = ( le ` K )
	dibfn.h	|- H = ( LHyp ` K )
	dibfn.i	|- I = ( ( DIsoB ` K ) ` W )
Assertion	dibdmN	|- ( ( K e. V /\ W e. H ) -> dom I = { x e. B | x .<_ W } )

Proof

Step	Hyp	Ref	Expression
1		dibfn.b	|- B = ( Base ` K )
2		dibfn.l	|- .<_ = ( le ` K )
3		dibfn.h	|- H = ( LHyp ` K )
4		dibfn.i	|- I = ( ( DIsoB ` K ) ` W )
5	1 2 3 4	dibfnN	|- ( ( K e. V /\ W e. H ) -> I Fn { x e. B | x .<_ W } )
6	5	fndmd	|- ( ( K e. V /\ W e. H ) -> dom I = { x e. B | x .<_ W } )