Theorem fimassd

Description: The image of a class is a subset of its codomain. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypothesis	fimassd.1	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
Assertion	fimassd	⊢ ( 𝜑 → ( 𝐹 “ 𝑋 ) ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		fimassd.1	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
2		fimass	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → ( 𝐹 “ 𝑋 ) ⊆ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐹 “ 𝑋 ) ⊆ 𝐵 )