Theorem nesymir 3057

Description: Inference associated with nesym 3055. (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 3002	. 2 ⊢ 𝐴 ≠ 𝐵
3	2	necomi 3053	1 ⊢ 𝐵 ≠ 𝐴

Syntax hints:  ¬ wn 3   = wceq 1656   ≠ wne 2999

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-ext 2803

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1879  df-cleq 2818  df-ne 3000

This theorem is referenced by:  relowlpssretop  33752