Theorem eldisjsim4

Description: Disjs implies element-disjoint range of QMap . Same as eldisjsim3 but expressed using the block-map range ran QMap R (often the more modular expression). (Contributed by Peter Mazsa, 15-Feb-2026)

	Ref	Expression
Assertion	eldisjsim4	|- ( R e. Disjs -> ran QMap R e. ElDisjs )

Proof

Step	Hyp	Ref	Expression
1		rnqmap	|- ran QMap R = ( dom R /. R )
2		eldisjsim3	|- ( R e. Disjs -> ( dom R /. R ) e. ElDisjs )
3	1 2	eqeltrid	|- ( R e. Disjs -> ran QMap R e. ElDisjs )