Theorem sstri

Description: Subclass transitivity inference. (Contributed by NM, 5-May-2000)

	Ref	Expression
Hypotheses	sstri.1	⊢ 𝐴 ⊆ 𝐵
	sstri.2	⊢ 𝐵 ⊆ 𝐶
Assertion	sstri	⊢ 𝐴 ⊆ 𝐶

Proof

Step	Hyp	Ref	Expression
1		sstri.1	⊢ 𝐴 ⊆ 𝐵
2		sstri.2	⊢ 𝐵 ⊆ 𝐶
3		sstr2	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐵 ⊆ 𝐶 → 𝐴 ⊆ 𝐶 ) )
4	1 2 3	mp2	⊢ 𝐴 ⊆ 𝐶