Theorem sstrdi

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

	Ref	Expression
Hypotheses	sstrdi.1	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
	sstrdi.2	⊢ 𝐵 ⊆ 𝐶
Assertion	sstrdi	⊢ ( 𝜑 → 𝐴 ⊆ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		sstrdi.1	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
2		sstrdi.2	⊢ 𝐵 ⊆ 𝐶
3	2	a1i	⊢ ( 𝜑 → 𝐵 ⊆ 𝐶 )
4	1 3	sstrd	⊢ ( 𝜑 → 𝐴 ⊆ 𝐶 )