Theorem eqsstrrdi

Description: A chained subclass and equality deduction. (Contributed by Mario Carneiro, 2-Jan-2017)

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

Proof

Step	Hyp	Ref	Expression
1		eqsstrrdi.1	⊢ ( 𝜑 → 𝐵 = 𝐴 )
2		eqsstrrdi.2	⊢ 𝐵 ⊆ 𝐶
3	1	eqcomd	⊢ ( 𝜑 → 𝐴 = 𝐵 )
4	3 2	eqsstrdi	⊢ ( 𝜑 → 𝐴 ⊆ 𝐶 )