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

Theorem class2seteq 4371
 Description: Equality theorem based on class2set 4370. (Contributed by NM, 13-Dec-2005.) (Proof shortened by Raph Levien, 30-Jun-2006.)
Assertion
Ref Expression
class2seteq
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem class2seteq
StepHypRef Expression
1 elex 2966 . 2
2 ax-1 6 . . . . 5
32ralrimiv 2790 . . . 4
4 rabid2 2887 . . . 4
53, 4sylibr 205 . . 3
65eqcomd 2443 . 2
71, 6syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726  wral 2707  crab 2711  cvv 2958 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-ral 2712  df-rab 2716  df-v 2960
 Copyright terms: Public domain W3C validator