Metamath Proof Explorer


Theorem nesymir

Description: Inference associated with nesym . (Contributed by BJ, 7-Jul-2018) (Proof shortened by Wolf Lammen, 25-Nov-2019)

Ref Expression
Hypothesis nesymir.1 ⊢ ¬ 𝐴 = 𝐵
Assertion nesymir 𝐵 ≠ 𝐴

Proof

Step Hyp Ref Expression
1 nesymir.1 ⊢ ¬ 𝐴 = 𝐵
2 1 neir ⊢ 𝐴 ≠ 𝐵
3 2 necomi ⊢ 𝐵 ≠ 𝐴