Theorem sseqtrrid

Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

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

Proof

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