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Theorem intsn 3806
 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 3805 . 2 (𝐴 ∈ V → {𝐴} = 𝐴)
31, 2ax-mp 5 1 {𝐴} = 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1331   ∈ wcel 1480  Vcvv 2686  {csn 3527  ∩ cint 3771 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-v 2688  df-un 3075  df-in 3077  df-sn 3533  df-pr 3534  df-int 3772 This theorem is referenced by:  uniintsnr  3807  intunsn  3809  op1stb  4399  op2ndb  5022  ssfii  6862
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