Theorem dmqmap

Description: QMap preserves the domain. Confirms that QMap is defined exactly on the points where cosets [ x ] R make sense (those in dom R ). (Contributed by Peter Mazsa, 14-Feb-2026)

	Ref	Expression
Assertion	dmqmap	Could not format assertion : No typesetting found for |- ( R e. V -> dom QMap R = dom R ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		df-qmap	Could not format QMap R = ( x e. dom R |-> [ x ] R ) : No typesetting found for |- QMap R = ( x e. dom R |-> [ x ] R ) with typecode |-
2		ecexg	$$⊢R\in V\to \left[x\right]R\in \mathrm{V}$$
3	2	adantr	$$⊢\left(R\in V\wedge x\in \mathrm{dom}R\right)\to \left[x\right]R\in \mathrm{V}$$
4	1 3	dmmptd	Could not format ( R e. V -> dom QMap R = dom R ) : No typesetting found for |- ( R e. V -> dom QMap R = dom R ) with typecode |-