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 )