Theorem sstrdi

Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypotheses	sstrdi.1	$$⊢\phi \to A\subseteq B$$
	sstrdi.2	$$⊢B\subseteq C$$
Assertion	sstrdi	$$⊢\phi \to A\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		sstrdi.1	$$⊢\phi \to A\subseteq B$$
2		sstrdi.2	$$⊢B\subseteq C$$
3	2	a1i	$$⊢\phi \to B\subseteq C$$
4	1 3	sstrd	$$⊢\phi \to A\subseteq C$$