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Theorem necon2i 2653
Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007.)
Hypothesis
Ref Expression
necon2i.1  |-  ( A  =  B  ->  C  =/=  D )
Assertion
Ref Expression
necon2i  |-  ( C  =  D  ->  A  =/=  B )

Proof of Theorem necon2i
StepHypRef Expression
1 necon2i.1 . . 3  |-  ( A  =  B  ->  C  =/=  D )
21neneqd 2619 . 2  |-  ( A  =  B  ->  -.  C  =  D )
32necon2ai 2651 1  |-  ( C  =  D  ->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653    =/= wne 2601
This theorem is referenced by:  cmpfi  17473  mcubic  20689  cubic2  20690  2sqlem11  21161  ovoliunnfl  26250  voliunnfl  26252  volsupnfl  26253  mncn0  27323  aaitgo  27346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 179  df-ne 2603
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