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Theorem neqcomd 2145
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 2142 . 2 (𝐴 = 𝐵𝐵 = 𝐴)
31, 2sylnib 666 1 (𝜑 → ¬ 𝐵 = 𝐴)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1332
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1424  ax-gen 1426  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-cleq 2133
This theorem is referenced by:  logbgcd1irraplemexp  13086
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