New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  oddnnul Unicode version

Theorem oddnnul 4509
 Description: An odd number is non-empty. (Contributed by SF, 22-Jan-2015.)
Assertion
Ref Expression
oddnnul Oddfin

Proof of Theorem oddnnul
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqeq1 2359 . . . . . 6 1c 1c
21rexbidv 2635 . . . . 5 Nn 1c Nn 1c
3 neeq1 2524 . . . . 5
42, 3anbi12d 691 . . . 4 Nn 1c Nn 1c
5 df-oddfin 4445 . . . 4 Oddfin Nn 1c
64, 5elab2g 2987 . . 3 Oddfin Oddfin Nn 1c
76ibi 232 . 2 Oddfin Nn 1c
87simprd 449 1 Oddfin
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wceq 1642   wcel 1710   wne 2516  wrex 2615  c0 3550  1cc1c 4134   Nn cnnc 4373   cplc 4375   Oddfin coddfin 4437 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-rex 2620  df-v 2861  df-oddfin 4445 This theorem is referenced by:  evenoddnnnul  4514  vinf  4555
 Copyright terms: Public domain W3C validator