Theorem sstrid

Description: Subclass transitivity deduction. (Contributed by NM, 6-Feb-2014)

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

Proof

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