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Theorem intsn 4318
 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 4317 . 2
31, 2ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1379   wcel 1767  cvv 3113  csn 4027  cint 4282 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-v 3115  df-un 3481  df-in 3483  df-sn 4028  df-pr 4030  df-int 4283 This theorem is referenced by:  uniintsn  4319  intunsn  4321  op1stb  4717  op2ndb  5490  ssfii  7875  cf0  8627  cflecard  8629  uffix  20157  iotain  30902
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