Description: Functionality and domain of the singleton of an ordered pair. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | fnsn.1 | ⊢ 𝐴 ∈ V | |
fnsn.2 | ⊢ 𝐵 ∈ V | ||
Assertion | fnsn | ⊢ { 〈 𝐴 , 𝐵 〉 } Fn { 𝐴 } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnsn.1 | ⊢ 𝐴 ∈ V | |
2 | fnsn.2 | ⊢ 𝐵 ∈ V | |
3 | fnsng | ⊢ ( ( 𝐴 ∈ V ∧ 𝐵 ∈ V ) → { 〈 𝐴 , 𝐵 〉 } Fn { 𝐴 } ) | |
4 | 1 2 3 | mp2an | ⊢ { 〈 𝐴 , 𝐵 〉 } Fn { 𝐴 } |