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Theorem class2set 4619
 Description: Construct, from any class , a set equal to it when the class exists and equal to the empty set when the class is proper. This theorem shows that the constructed set always exists. (Contributed by NM, 16-Oct-2003.)
Assertion
Ref Expression
class2set
Distinct variable group:   ,

Proof of Theorem class2set
StepHypRef Expression
1 rabexg 4602 . 2
2 simpl 457 . . . . 5
32nrexdv 2913 . . . 4
4 rabn0 3805 . . . . 5
54necon1bbii 2721 . . . 4
63, 5sylib 196 . . 3
7 0ex 4582 . . 3
86, 7syl6eqel 2553 . 2
91, 8pm2.61i 164 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  =wceq 1395  e.wcel 1818  E.wrex 2808  {crab 2811   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  ax-sep 4573  ax-nul 4581 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-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785
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