Theorem fnmpompt

Description: Characterization of the outer domain of a chained maps-to expression. (Contributed by Zhi Wang, 14-Sep-2026)

	Ref	Expression
Hypothesis	fnmpompt.l	$$⊢L=\left(u\in B,v\in B⟼\left(a\in \left(uHv\right)⟼A\left(a\right)\right)\right)$$
Assertion	fnmpompt	$$⊢LFn\left(B\times B\right)$$

Proof

Step	Hyp	Ref	Expression
1		fnmpompt.l	$$⊢L=\left(u\in B,v\in B⟼\left(a\in \left(uHv\right)⟼A\left(a\right)\right)\right)$$
2		ovex	$$⊢uHv\in \mathrm{V}$$
3	2	mptex	$$⊢\left(a\in \left(uHv\right)⟼A\left(a\right)\right)\in \mathrm{V}$$
4	1 3	fnmpoi	$$⊢LFn\left(B\times B\right)$$