Theorem aovnfundmuv

Description: If an ordered pair is not in the domain of a class or the class is not a function restricted to the ordered pair, then the operation value for this pair is the universal class. (Contributed by Alexander van der Vekens, 26-May-2017)

	Ref	Expression
Assertion	aovnfundmuv	$$⊢\neg F\mathrm{defAt}⟨A,B⟩\to ((AFB))=\mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		df-aov	$$⊢((AFB))=\left(F\mathrm{\text{'}\text{'}\text{'}}⟨A,B⟩\right)$$
2		afvnfundmuv	$$⊢\neg F\mathrm{defAt}⟨A,B⟩\to \left(F\mathrm{\text{'}\text{'}\text{'}}⟨A,B⟩\right)=\mathrm{V}$$
3	1 2	eqtrid	$$⊢\neg F\mathrm{defAt}⟨A,B⟩\to ((AFB))=\mathrm{V}$$