Metamath Proof Explorer


Theorem f1dom

Description: The domain of a one-to-one function is dominated by its codomain. (Contributed by NM, 19-Jun-1998)

Ref Expression
Hypothesis f1dom.1 ⊢ B ∈ V
Assertion f1dom ⊢ F : A ⟶ 1-1 B → A ≼ B

Proof

Step Hyp Ref Expression
1 f1dom.1 ⊢ B ∈ V
2 f1domg ⊢ B ∈ V → F : A ⟶ 1-1 B → A ≼ B
3 1 2 ax-mp ⊢ F : A ⟶ 1-1 B → A ≼ B