MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  necon2d Unicode version

Theorem necon2d 2683
Description: Contrapositive inference for inequality. (Contributed by NM, 28-Dec-2008.)
Hypothesis
Ref Expression
necon2d.1
Assertion
Ref Expression
necon2d

Proof of Theorem necon2d
StepHypRef Expression
1 necon2d.1 . . 3
2 df-ne 2654 . . 3
31, 2syl6ib 226 . 2
43necon2ad 2670 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  =wceq 1395  =/=wne 2652
This theorem is referenced by:  map0g  7478  cantnf  8133  cantnfOLD  8155  hashprg  12460  bcthlem5  21767  deg1ldgn  22493  cxpeq0  23059  islshpat  34742  cdleme18b  36017  cdlemh  36543
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 2654
  Copyright terms: Public domain W3C validator