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Theorem intsn 3901
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 3900 . 2 (𝐴 ∈ V → {𝐴} = 𝐴)
31, 2ax-mp 5 1 {𝐴} = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1364  wcel 2160  Vcvv 2756  {csn 3614   cint 3866
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-v 2758  df-un 3153  df-in 3155  df-sn 3620  df-pr 3621  df-int 3867
This theorem is referenced by:  uniintsnr  3902  intunsn  3904  op1stb  4503  op2ndb  5137  ssfii  7019
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