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Theorem abexv 4324
 Description: When does not occur in , is a set. (Contributed by SF, 17-Jan-2015.)
Assertion
Ref Expression
abexv
Distinct variable group:   ,

Proof of Theorem abexv
StepHypRef Expression
1 abvor0 3567 . 2
2 vvex 4109 . . . 4
3 eleq1 2413 . . . 4
42, 3mpbiri 224 . . 3
5 0ex 4110 . . . 4
6 eleq1 2413 . . . 4
75, 6mpbiri 224 . . 3
84, 7jaoi 368 . 2
91, 8ax-mp 8 1
 Colors of variables: wff setvar class Syntax hints:   wo 357   wceq 1642   wcel 1710  cab 2339  cvv 2859  c0 3550 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  ax-nin 4078 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-un 3214  df-dif 3215  df-ss 3259  df-nul 3551 This theorem is referenced by:  nncaddccl  4419  preaddccan2lem1  4454  ltfintrilem1  4465  leconnnc  6218  addccan2nclem2  6264  nchoicelem16  6304
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