Theorem sseq2i

Description: An equality inference for the subclass relationship. (Contributed by NM, 30-Aug-1993)

	Ref	Expression
Hypothesis	sseq1i.1	⊢ 𝐴 = 𝐵
Assertion	sseq2i	⊢ ( 𝐶 ⊆ 𝐴 ↔ 𝐶 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		sseq1i.1	⊢ 𝐴 = 𝐵
2		sseq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 ⊆ 𝐴 ↔ 𝐶 ⊆ 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐶 ⊆ 𝐴 ↔ 𝐶 ⊆ 𝐵 )