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Theorem neqcomd 2834
Description: Commute an inequality. (Contributed by Rohan Ridenour, 3-Aug-2023.)
Hypothesis
Ref Expression
neqcomd.1 (𝜑 → ¬ 𝐴 = 𝐵)
Assertion
Ref Expression
neqcomd (𝜑 → ¬ 𝐵 = 𝐴)

Proof of Theorem neqcomd
StepHypRef Expression
1 neqcomd.1 . 2 (𝜑 → ¬ 𝐴 = 𝐵)
2 eqcom 2831 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
31, 2sylnib 331 1 (𝜑 → ¬ 𝐵 = 𝐴)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1538
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 1912  ax-6 1971  ax-7 2016  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-cleq 2817
This theorem is referenced by:  phpeqd  8703  simpgnsgd  19222  rr-phpd  40836
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