Theorem sstrid

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

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

Proof

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