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Theorem intsn 4086
 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
Assertion
Ref Expression
intsn

Proof of Theorem intsn
StepHypRef Expression
1 intsn.1 . 2
2 intsng 4085 . 2
31, 2ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cvv 2956  csn 3814  cint 4050 This theorem is referenced by:  uniintsn  4087  intunsn  4089  op1stb  4758  op2ndb  5353  ssfii  7424  cf0  8131  cflecard  8133  uffix  17953  iotain  27594 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-v 2958  df-un 3325  df-in 3327  df-sn 3820  df-pr 3821  df-int 4051
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