Theorem sneqi

Description: Equality inference for singletons. (Contributed by NM, 22-Jan-2004)

	Ref	Expression
Hypothesis	sneqi.1	⊢ 𝐴 = 𝐵
Assertion	sneqi	⊢ { 𝐴 } = { 𝐵 }

Proof

Step	Hyp	Ref	Expression
1		sneqi.1	⊢ 𝐴 = 𝐵
2		sneq	⊢ ( 𝐴 = 𝐵 → { 𝐴 } = { 𝐵 } )
3	1 2	ax-mp	⊢ { 𝐴 } = { 𝐵 }