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Metamath Proof Explorer

Theorem fconstmpo

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

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

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