Theorem nesymir 2999

Description: Inference associated with nesym 2997. (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 2943	. 2 ⊢ 𝐴 ≠ 𝐵
3	2	necomi 2995	1 ⊢ 𝐵 ≠ 𝐴

Syntax hints:  ¬ wn 3   = wceq 1539   ≠ wne 2940

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1910  ax-6 1967  ax-7 2007  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-cleq 2729  df-ne 2941

This theorem is referenced by:  relowlpssretop  37359