Metamath Proof Explorer


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 }