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Theorem intsn 4874
Description: The intersection of a singleton is its member. Theorem 70 of [Suppes] p. 41. (Contributed by NM, 29-Sep-2002.)
Hypothesis
Ref Expression
intsn.1 𝐴 ∈ V
Assertion
Ref Expression
intsn {𝐴} = 𝐴

Proof of Theorem intsn
StepHypRef Expression
1 intsn.1 . 2 𝐴 ∈ V
2 intsng 4873 . 2 (𝐴 ∈ V → {𝐴} = 𝐴)
31, 2ax-mp 5 1 {𝐴} = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wcel 2114  Vcvv 3398  {csn 4516   cint 4836
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-ral 3058  df-v 3400  df-un 3848  df-in 3850  df-sn 4517  df-pr 4519  df-int 4837
This theorem is referenced by:  uniintsn  4875  intunsn  4877  op1stb  5329  op2ndb  6059  ssfii  8958  cf0  9753  cflecard  9755  uffix  22674  iotain  41595
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