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Metamath Proof Explorer

Theorem funsn

Description: A singleton of an ordered pair is a function. Theorem 10.5 of Quine p. 65. (Contributed by NM, 12-Aug-1994)

Ref Expression
Hypotheses funsn.1 ⊢ A ∈ V
funsn.2 ⊢ B ∈ V
Assertion funsn ⊢ Fun ⁡ A B

Proof

Step Hyp Ref Expression
1 funsn.1 ⊢ A ∈ V
2 funsn.2 ⊢ B ∈ V
3 funsng ⊢ A ∈ V ∧ B ∈ V → Fun ⁡ A B
4 1 2 3 mp2an ⊢ Fun ⁡ A B