Theorem sseq1i

Description: An equality inference for the subclass relationship. (Contributed by NM, 18-Aug-1993)

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

Proof

Step	Hyp	Ref	Expression
1		sseq1i.1	⊢ 𝐴 = 𝐵
2		sseq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ⊆ 𝐶 ↔ 𝐵 ⊆ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ⊆ 𝐶 ↔ 𝐵 ⊆ 𝐶 )