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Theorem intsng 3640
Description: Intersection of a singleton. (Contributed by Stefan O'Rear, 22-Feb-2015.)
Assertion
Ref Expression
intsng  V  |^| { }

Proof of Theorem intsng
StepHypRef Expression
1 dfsn2 3381 . . 3  { }  { ,  }
21inteqi 3610 . 2  |^| { }  |^| { ,  }
3 intprg 3639 . . . 4  V  V  |^| { ,  }  i^i
43anidms 377 . . 3  V  |^| { ,  }  i^i
5 inidm 3140 . . 3  i^i
64, 5syl6eq 2085 . 2  V  |^| { ,  }
72, 6syl5eq 2081 1  V  |^| { }
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   wcel 1390    i^i cin 2910   {csn 3367   {cpr 3368   |^|cint 3606
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-un 2916  df-in 2918  df-sn 3373  df-pr 3374  df-int 3607
This theorem is referenced by:  intsn  3641  op1stbg  4176  riinint  4536
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