MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  necon1abii Unicode version

Theorem necon1abii 2719
Description: Contrapositive inference for inequality. (Contributed by NM, 17-Mar-2007.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)
Hypothesis
Ref Expression
necon1abii.1
Assertion
Ref Expression
necon1abii

Proof of Theorem necon1abii
StepHypRef Expression
1 notnot 291 . 2
2 necon1abii.1 . . 3
32necon3bbii 2718 . 2
41, 3bitr2i 250 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  =wceq 1395  =/=wne 2652
This theorem is referenced by:  necon2abii  2723  marypha1lem  7913  npomex  9395  uniinn0  27424
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