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Theorem clel2 2975
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 2413 . . 3
31, 2ceqsalv 2885 . 2
43bicomi 193 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176  wal 1540   wceq 1642   wcel 1710  cvv 2859
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861
This theorem is referenced by:  snss  3838
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