Theorem imass2d

Description: Subset theorem for image. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	imass2d.1	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
Assertion	imass2d	⊢ ( 𝜑 → ( 𝐶 “ 𝐴 ) ⊆ ( 𝐶 “ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		imass2d.1	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
2		imass2	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐶 “ 𝐴 ) ⊆ ( 𝐶 “ 𝐵 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐶 “ 𝐴 ) ⊆ ( 𝐶 “ 𝐵 ) )