Theorem sseqtrrdi

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

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

Proof

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