Theorem nesymir 3045

Description: Inference associated with nesym 3043. (Contributed by BJ, 7-Jul-2018.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)

Hypothesis

Ref	Expression
nesymir.1	⊢ ¬ 𝐴 = 𝐵

Assertion

Ref	Expression
nesymir	⊢ 𝐵 ≠ 𝐴

Proof of Theorem nesymir

Step	Hyp	Ref	Expression
1		nesymir.1	. . 3 ⊢ ¬ 𝐴 = 𝐵
2	1	neir 2990	. 2 ⊢ 𝐴 ≠ 𝐵
3	2	necomi 3041	1 ⊢ 𝐵 ≠ 𝐴

Syntax hints:  ¬ wn 3   = wceq 1538   ≠ wne 2987

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-9 2121  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-cleq 2791  df-ne 2988

This theorem is referenced by:  relowlpssretop  34781