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Theorem risset 2346
 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 1496 . 2 (x(x B x = A) ↔ x(x = A x B))
2 df-rex 2306 . 2 (x B x = Ax(x B x = A))
3 df-clel 2033 . 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 1242  ∃wex 1378   ∈ wcel 1390  ∃wrex 2301 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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424 This theorem depends on definitions:  df-bi 110  df-clel 2033  df-rex 2306 This theorem is referenced by:  reueq  2732  reuind  2738  0el  3235  iunid  3703  sucel  4113  reusv3  4158  fvmptt  5205  releldm2  5753  qsid  6107  rerecclap  7468  nndiv  7715  zq  8317  4fvwrd4  8747  bj-bdcel  9272
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