New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  abvor0 Unicode version

Theorem abvor0 3567
 Description: The class builder of a wff not containing the abstraction variable is either the universal class or the empty set. (Contributed by Mario Carneiro, 29-Aug-2013.)
Assertion
Ref Expression
abvor0
Distinct variable group:   ,

Proof of Theorem abvor0
StepHypRef Expression
1 id 19 . . . . . 6
2 vex 2862 . . . . . . 7
32a1i 10 . . . . . 6
41, 32thd 231 . . . . 5
54abbi1dv 2469 . . . 4
65con3i 127 . . 3
7 id 19 . . . . 5
8 noel 3554 . . . . . 6
98a1i 10 . . . . 5
107, 92falsed 340 . . . 4
1110abbi1dv 2469 . . 3
126, 11syl 15 . 2
1312orri 365 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wo 357   wceq 1642   wcel 1710  cab 2339  cvv 2859  c0 3550 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-nan 1288  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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-nul 3551 This theorem is referenced by:  abexv  4324
 Copyright terms: Public domain W3C validator