Theorem frnd

Description: Deduction form of frn . The range of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	frnd.1	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
Assertion	frnd	⊢ ( 𝜑 → ran 𝐹 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		frnd.1	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
2		frn	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → ran 𝐹 ⊆ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → ran 𝐹 ⊆ 𝐵 )