Theorem ndmaov

Description: The value of an operation outside its domain, analogous to ndmafv . (Contributed by Alexander van der Vekens, 26-May-2017)

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

Proof

Step	Hyp	Ref	Expression
1		df-aov	$$⊢((AFB))=\left(F\mathrm{\text{'}\text{'}\text{'}}⟨A,B⟩\right)$$
2		ndmafv	$$⊢\neg ⟨A,B⟩\in \mathrm{dom}F\to \left(F\mathrm{\text{'}\text{'}\text{'}}⟨A,B⟩\right)=\mathrm{V}$$
3	1 2	syl5eq	$$⊢\neg ⟨A,B⟩\in \mathrm{dom}F\to ((AFB))=\mathrm{V}$$