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Theorem class2seteq 4360
 Description: Equality theorem based on class2set 4359. (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 2956 . 2
2 ax-1 5 . . . . 5
32ralrimiv 2780 . . . 4
4 rabid2 2877 . . . 4
53, 4sylibr 204 . . 3
65eqcomd 2440 . 2
71, 6syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wral 2697  crab 2701  cvv 2948 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 This theorem depends on definitions:  df-bi 178  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-ral 2702  df-rab 2706  df-v 2950
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