Theorem eqsstrrid

Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004)

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

Proof

Step	Hyp	Ref	Expression
1		eqsstrrid.1	⊢ 𝐵 = 𝐴
2		eqsstrrid.2	⊢ ( 𝜑 → 𝐵 ⊆ 𝐶 )
3	1	eqcomi	⊢ 𝐴 = 𝐵
4	3 2	eqsstrid	⊢ ( 𝜑 → 𝐴 ⊆ 𝐶 )