Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  class2seteq Unicode version

Theorem class2seteq 4620
 Description: Equality theorem based on class2set 4619. (Contributed by NM, 13-Dec-2005.) (Proof shortened by Raph Levien, 30-Jun-2006.)
Assertion
Ref Expression
class2seteq
Distinct variable group:   ,

Proof of Theorem class2seteq
StepHypRef Expression
1 elex 3118 . 2
2 ax-1 6 . . . . 5
32ralrimiv 2869 . . . 4
4 rabid2 3035 . . . 4
53, 4sylibr 212 . . 3
65eqcomd 2465 . 2
71, 6syl 16 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  A.wral 2807  {crab 2811   cvv 3109 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-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-rab 2816  df-v 3111
 Copyright terms: Public domain W3C validator