Theorem fun0

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 ∅

Proof

Step	Hyp	Ref	Expression
1		0ss	⊢ ∅ ⊆ { ⟨ ∅ , ∅ ⟩ }
2		0ex	⊢ ∅ ∈ V
3	2 2	funsn	⊢ Fun { ⟨ ∅ , ∅ ⟩ }
4		funss	⊢ ( ∅ ⊆ { ⟨ ∅ , ∅ ⟩ } → ( Fun { ⟨ ∅ , ∅ ⟩ } → Fun ∅ ) )
5	1 3 4	mp2	⊢ Fun ∅