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Theorem abf 3819
 Description: A class builder with a false argument is empty. (Contributed by NM, 20-Jan-2012.)
Hypothesis
Ref Expression
abf.1
Assertion
Ref Expression
abf

Proof of Theorem abf
StepHypRef Expression
1 abf.1 . . . 4
21pm2.21i 131 . . 3
32abssi 3574 . 2
4 ss0 3816 . 2
53, 4ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  =wceq 1395  e.wcel 1818  {cab 2442  C_wss 3475   c0 3784 This theorem is referenced by:  csbprc  3821  mpt20  6367  fi0  7900  meet0  15767  join0  15768  rusgra0edg  24955  pmapglb2xN  35496 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-in 3482  df-ss 3489  df-nul 3785
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