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Theorem evennnul 4508
 Description: An even number is nonempty. (Contributed by SF, 22-Jan-2015.)
Assertion
Ref Expression
evennnul Evenfin

Proof of Theorem evennnul
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqeq1 2359 . . . . . 6
21rexbidv 2635 . . . . 5 Nn Nn
3 neeq1 2524 . . . . 5
42, 3anbi12d 691 . . . 4 Nn Nn
5 df-evenfin 4444 . . . 4 Evenfin Nn
64, 5elab2g 2987 . . 3 Evenfin Evenfin Nn
76ibi 232 . 2 Evenfin Nn
87simprd 449 1 Evenfin
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wceq 1642   wcel 1710   wne 2516  wrex 2615  c0 3550   Nn cnnc 4373   cplc 4375   Evenfin cevenfin 4436 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-evenfin 4444 This theorem is referenced by:  evenoddnnnul  4514  vinf  4555
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