Theorem fimass

Description: The image of a class under a function with domain and codomain is a subset of its codomain. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Assertion	fimass	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → ( 𝐹 “ 𝑋 ) ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		imassrn	⊢ ( 𝐹 “ 𝑋 ) ⊆ ran 𝐹
2		frn	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → ran 𝐹 ⊆ 𝐵 )
3	1 2	sstrid	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → ( 𝐹 “ 𝑋 ) ⊆ 𝐵 )