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 AV
funsn.2 BV
Assertion funsn FunAB

Proof

Step Hyp Ref Expression
1 funsn.1 AV
2 funsn.2 BV
3 funsng AVBVFunAB
4 1 2 3 mp2an FunAB