Theorem fconstmpo

Description: Representation of a constant operation using the mapping operation. (Contributed by SO, 11-Jul-2018)

	Ref	Expression
Assertion	fconstmpo	$$⊢\left(A\times B\right)\times \left\{C\right\}=\left(x\in A,y\in B⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		fconstmpt	$$⊢\left(A\times B\right)\times \left\{C\right\}=\left(z\in \left(A\times B\right)⟼C\right)$$
2		eqidd	$$⊢z=⟨x,y⟩\to C=C$$
3	2	mpompt	$$⊢\left(z\in \left(A\times B\right)⟼C\right)=\left(x\in A,y\in B⟼C\right)$$
4	1 3	eqtri	$$⊢\left(A\times B\right)\times \left\{C\right\}=\left(x\in A,y\in B⟼C\right)$$