Theorem sseqtrri

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 4-Apr-1995)

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

Proof

Step	Hyp	Ref	Expression
1		sseqtrri.1	⊢ 𝐴 ⊆ 𝐵
2		sseqtrri.2	⊢ 𝐶 = 𝐵
3	2	eqcomi	⊢ 𝐵 = 𝐶
4	1 3	sseqtri	⊢ 𝐴 ⊆ 𝐶