Theorem eqsstri

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 16-Jul-1995)

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

Proof

Step	Hyp	Ref	Expression
1		eqsstr.1	⊢ 𝐴 = 𝐵
2		eqsstr.2	⊢ 𝐵 ⊆ 𝐶
3	1	sseq1i	⊢ ( 𝐴 ⊆ 𝐶 ↔ 𝐵 ⊆ 𝐶 )
4	2 3	mpbir	⊢ 𝐴 ⊆ 𝐶