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Theorem clel3 2977
 Description: An alternate definition of class membership when the class is a set. (Contributed by NM, 18-Aug-1993.)
Hypothesis
Ref Expression
clel3.1 B V
Assertion
Ref Expression
clel3 (A Bx(x = B A x))
Distinct variable groups:   x,A   x,B

Proof of Theorem clel3
StepHypRef Expression
1 clel3.1 . 2 B V
2 clel3g 2976 . 2 (B V → (A Bx(x = B A x)))
31, 2ax-mp 5 1 (A Bx(x = B A x))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358  ∃wex 1541   = wceq 1642   ∈ wcel 1710  Vcvv 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-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by:  unipr  3905  nnsucelrlem1  4424  tfinnnlem1  4533  dfop2lem1  4573  setconslem2  4732  nenpw1pwlem1  6084
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