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Theorem abvor0 3485
 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 2804 . . . . . . 7
32a1i 10 . . . . . 6
41, 32thd 231 . . . . 5
54abbi1dv 2412 . . . 4
65con3i 127 . . 3
7 id 19 . . . . 5
8 noel 3472 . . . . . 6
98a1i 10 . . . . 5
107, 92falsed 340 . . . 4
1110abbi1dv 2412 . . 3
126, 11syl 15 . 2
1312orri 365 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 357   wceq 1632   wcel 1696  cab 2282  cvv 2801  c0 3468 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-nul 3469
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