This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem f10

Description: The empty set maps one-to-one into any class. (Contributed by NM, 7-Apr-1998)

Ref Expression
Assertion f10 ⊢ ∅ : ∅ ⟶ 1-1 A

Proof

Step Hyp Ref Expression
1 f0 ⊢ ∅ : ∅ ⟶ A
2 funcnv0 ⊢ Fun ⁡ ∅ -1
3 df-f1 ⊢ ∅ : ∅ ⟶ 1-1 A ↔ ∅ : ∅ ⟶ A ∧ Fun ⁡ ∅ -1
4 1 2 3 mpbir2an ⊢ ∅ : ∅ ⟶ 1-1 A