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Theorem class2set 4359
 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 4345 . 2
2 simpl 444 . . . . 5
32nrexdv 2801 . . . 4
4 rabn0 3639 . . . . 5
54necon1bbii 2650 . . . 4
63, 5sylib 189 . . 3
7 0ex 4331 . . 3
86, 7syl6eqel 2523 . 2
91, 8pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1652   wcel 1725  wrex 2698  crab 2701  cvv 2948  c0 3620 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621
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