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Theorem intsn 4989
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 4988 . 2 (𝐴 ∈ V → {𝐴} = 𝐴)
31, 2ax-mp 5 1 {𝐴} = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1541  wcel 2106  Vcvv 3474  {csn 4627   cint 4949
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-ral 3062  df-rex 3071  df-v 3476  df-un 3952  df-in 3954  df-sn 4628  df-pr 4630  df-int 4950
This theorem is referenced by:  uniintsn  4990  intunsn  4992  op1stb  5470  op2ndb  6223  ssfii  9410  cf0  10242  cflecard  10244  uffix  23416  iotain  43161
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