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 ⟩ }