Theorem sseqtri

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 28-Jul-1995)

	Ref	Expression
Hypotheses	sseqtr.1	⊢ 𝐴 ⊆ 𝐵
	sseqtr.2	⊢ 𝐵 = 𝐶
Assertion	sseqtri	⊢ 𝐴 ⊆ 𝐶

Proof

Step	Hyp	Ref	Expression
1		sseqtr.1	⊢ 𝐴 ⊆ 𝐵
2		sseqtr.2	⊢ 𝐵 = 𝐶
3	2	sseq2i	⊢ ( 𝐴 ⊆ 𝐵 ↔ 𝐴 ⊆ 𝐶 )
4	1 3	mpbi	⊢ 𝐴 ⊆ 𝐶