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Theorem risset 2330
Description: Two ways to say "A belongs to B." (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
risset (A Bx B x = A)
Distinct variable groups:   x,A   x,B

Proof of Theorem risset
StepHypRef Expression
1 exancom 1481 . 2 (x(x B x = A) ↔ x(x = A x B))
2 df-rex 2290 . 2 (x B x = Ax(x B x = A))
3 df-clel 2018 . 2 (A Bx(x = A x B))
41, 2, 33bitr4ri 202 1 (A Bx B x = A)
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98   = wceq 1228  wex 1362   wcel 1374  wrex 2285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-ial 1409
This theorem depends on definitions:  df-bi 110  df-clel 2018  df-rex 2290
This theorem is referenced by:  reueq  2715  reuind  2721  0el  3218  iunid  3686  sucel  4096  reusv3  4142  fvmptt  5187  releldm2  5734  qsid  6082  bj-bdcel  7211
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