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Theorem abvor0 3803
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 22 . . . . . 6
2 vex 3112 . . . . . . 7
32a1i 11 . . . . . 6
41, 32thd 240 . . . . 5
54abbi1dv 2595 . . . 4
65con3i 135 . . 3
7 id 22 . . . . 5
8 noel 3788 . . . . . 6
98a1i 11 . . . . 5
107, 92falsed 351 . . . 4
1110abbi1dv 2595 . . 3
126, 11syl 16 . 2
1312orri 376 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  \/wo 368  =wceq 1395  e.wcel 1818  {cab 2442   cvv 3109   c0 3784
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-dif 3478  df-nul 3785
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