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Theorem necon1i 2490
Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007.)
Hypothesis
Ref Expression
necon1i.1  |-  ( A  =/=  B  ->  C  =  D )
Assertion
Ref Expression
necon1i  |-  ( C  =/=  D  ->  A  =  B )

Proof of Theorem necon1i
StepHypRef Expression
1 df-ne 2448 . . 3  |-  ( A  =/=  B  <->  -.  A  =  B )
2 necon1i.1 . . 3  |-  ( A  =/=  B  ->  C  =  D )
31, 2sylbir 204 . 2  |-  ( -.  A  =  B  ->  C  =  D )
43necon1ai 2488 1  |-  ( C  =/=  D  ->  A  =  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1623    =/= wne 2446
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 177  df-ne 2448
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