Theorem sstr

Description: Transitivity of subclass relationship. Theorem 6 of Suppes p. 23. (Contributed by NM, 5-Sep-2003)

	Ref	Expression
Assertion	sstr	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ 𝐵 ⊆ 𝐶 ) → 𝐴 ⊆ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		sstr2	⊢ ( 𝐴 ⊆ 𝐵 → ( 𝐵 ⊆ 𝐶 → 𝐴 ⊆ 𝐶 ) )
2	1	imp	⊢ ( ( 𝐴 ⊆ 𝐵 ∧ 𝐵 ⊆ 𝐶 ) → 𝐴 ⊆ 𝐶 )