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Theorem neqcomd 2175
Description: Commute an inequality. (Contributed by Rohan Ridenour, 3-Aug-2023.)
Hypothesis
Ref Expression
neqcomd.1  |-  ( ph  ->  -.  A  =  B )
Assertion
Ref Expression
neqcomd  |-  ( ph  ->  -.  B  =  A )

Proof of Theorem neqcomd
StepHypRef Expression
1 neqcomd.1 . 2  |-  ( ph  ->  -.  A  =  B )
2 eqcom 2172 . 2  |-  ( A  =  B  <->  B  =  A )
31, 2sylnib 671 1  |-  ( ph  ->  -.  B  =  A )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1348
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 609  ax-in2 610  ax-5 1440  ax-gen 1442  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-cleq 2163
This theorem is referenced by:  logbgcd1irraplemexp  13645
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