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

Step	Hyp	Ref	Expression
1		rabexg 4602	. 2
2		simpl 457	. . . . 5
3	2	nrexdv 2913	. . . 4
4		rabn0 3805	. . . . 5
5	4	necon1bbii 2721	. . . 4
6	3, 5	sylib 196	. . 3
7		0ex 4582	. . 3
8	6, 7	syl6eqel 2553	. 2
9	1, 8	pm2.61i 164	1

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