Theorem imass2d

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

	Ref	Expression
Hypothesis	imass2d.1	$$⊢\phi \to A\subseteq B$$
Assertion	imass2d	$$⊢\phi \to C\left[A\right]\subseteq C\left[B\right]$$

Proof

Step	Hyp	Ref	Expression
1		imass2d.1	$$⊢\phi \to A\subseteq B$$
2		imass2	$$⊢A\subseteq B\to C\left[A\right]\subseteq C\left[B\right]$$
3	1 2	syl	$$⊢\phi \to C\left[A\right]\subseteq C\left[B\right]$$