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 〉 } |
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 〉 } |