Theorem eqsstrdi

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

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

Proof

Step	Hyp	Ref	Expression
1		eqsstrdi.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		eqsstrdi.2	⊢ 𝐵 ⊆ 𝐶
3	2	a1i	⊢ ( 𝜑 → 𝐵 ⊆ 𝐶 )
4	1 3	eqsstrd	⊢ ( 𝜑 → 𝐴 ⊆ 𝐶 )