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Theorem necon2i 2648
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 2614 . 2  |-  ( A  =  B  ->  -.  C  =  D )
32necon2ai 2646 1  |-  ( C  =  D  ->  A  =/=  B )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1362    =/= wne 2596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-ne 2598
This theorem is referenced by:  cmpfi  18853  mcubic  22127  cubic2  22128  2sqlem11  22599  ovoliunnfl  28277  voliunnfl  28279  volsupnfl  28280  mncn0  29341  aaitgo  29364
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