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Theorem clel2 3064
 Description: An alternate definition of class membership when the class is a set. (Contributed by NM, 18-Aug-1993.)
Hypothesis
Ref Expression
clel2.1
Assertion
Ref Expression
clel2
Distinct variable groups:   ,   ,

Proof of Theorem clel2
StepHypRef Expression
1 clel2.1 . . 3
2 eleq1 2495 . . 3
31, 2ceqsalv 2974 . 2
43bicomi 194 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wceq 1652   wcel 1725  cvv 2948 This theorem is referenced by:  snss  3918  mptelee  25799 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-11 1761  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950
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