Description: The empty set is a function. Theorem 10.3 of Quine p. 65. (Contributed by NM, 7-Apr-1998)
Ref | Expression | ||
---|---|---|---|
Assertion | fun0 | ⊢ Fun ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ss | ⊢ ∅ ⊆ { 〈 ∅ , ∅ 〉 } | |
2 | 0ex | ⊢ ∅ ∈ V | |
3 | 2 2 | funsn | ⊢ Fun { 〈 ∅ , ∅ 〉 } |
4 | funss | ⊢ ( ∅ ⊆ { 〈 ∅ , ∅ 〉 } → ( Fun { 〈 ∅ , ∅ 〉 } → Fun ∅ ) ) | |
5 | 1 3 4 | mp2 | ⊢ Fun ∅ |