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Metamath Proof Explorer

Theorem mapval

Description: The value of set exponentiation (inference version). ( A ^m B ) is the set of all functions that map from B to A . Definition 10.24 of Kunen p. 24. (Contributed by NM, 8-Dec-2003)

Ref Expression
Hypotheses mapval.1 ⊢ A ∈ V
mapval.2 ⊢ B ∈ V
Assertion mapval ⊢ A B = f | f : B ⟶ A

Proof

Step Hyp Ref Expression
1 mapval.1 ⊢ A ∈ V
2 mapval.2 ⊢ B ∈ V
3 mapvalg ⊢ A ∈ V ∧ B ∈ V → A B = f | f : B ⟶ A
4 1 2 3 mp2an ⊢ A B = f | f : B ⟶ A