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Theorem intsn 3962
 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 3961 . 2 (A V → {A} = A)
31, 2ax-mp 8 1 {A} = A
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∈ wcel 1710  Vcvv 2859  {csn 3737  ∩cint 3926 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-sn 3741  df-pr 3742  df-int 3927 This theorem is referenced by:  uniintsn  3963  intunsn  3965
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