Theorem sylan9ssr

Description: A subclass transitivity deduction. (Contributed by NM, 27-Sep-2004)

	Ref	Expression
Hypotheses	sylan9ssr.1	$$⊢\phi \to A\subseteq B$$
	sylan9ssr.2	$$⊢\psi \to B\subseteq C$$
Assertion	sylan9ssr	$$⊢\left(\psi \wedge \phi \right)\to A\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		sylan9ssr.1	$$⊢\phi \to A\subseteq B$$
2		sylan9ssr.2	$$⊢\psi \to B\subseteq C$$
3	1 2	sylan9ss	$$⊢\left(\phi \wedge \psi \right)\to A\subseteq C$$
4	3	ancoms	$$⊢\left(\psi \wedge \phi \right)\to A\subseteq C$$