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Metamath Proof Explorer

Theorem fvconst2g

Description: The value of a constant function. (Contributed by NM, 20-Aug-2005)

		Ref	Expression
	Assertion	fvconst2g	$⊢ (B \in D \land C \in A) \to (A \times \{B\}) (C) = B$

Step	Hyp	Ref	Expression
1		fconstg	$⊢ B \in D \to (A \times \{B\}) : A ⟶ \{B\}$
2		fvconst	$⊢ ((A \times \{B\}) : A ⟶ \{B\} \land C \in A) \to (A \times \{B\}) (C) = B$
3	1 2	sylan	$⊢ (B \in D \land C \in A) \to (A \times \{B\}) (C) = B$