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Theorem nonconne 2661
Description: Law of noncontradiction with equality and inequality. (Contributed by NM, 3-Feb-2012.) (Proof shortened by Wolf Lammen, 21-Dec-2019.)
Assertion
Ref Expression
nonconne

Proof of Theorem nonconne
StepHypRef Expression
1 fal 1377 . 2
2 eqneqall 2660 . . 3
32imp 429 . 2
41, 3mto 176 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  /\wa 369  =wceq 1370   wfal 1375  =/=wne 2648
This theorem is referenced by:  osumcllem11N  34461  pexmidlem8N  34472  dochexmidlem8  35963
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-an 371  df-tru 1373  df-fal 1376  df-ne 2650
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