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Theorem rint0 3645
Description: Relative intersection of an empty set. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
rint0  X  (/)  i^i  |^| X

Proof of Theorem rint0
StepHypRef Expression
1 inteq 3609 . . 3  X  (/)  |^| X  |^| (/)
21ineq2d 3132 . 2  X  (/)  i^i  |^| X  i^i  |^| (/)
3 int0 3620 . . . 4  |^| (/)  _V
43ineq2i 3129 . . 3  i^i  |^| (/)  i^i  _V
5 inv1 3247 . . 3  i^i  _V
64, 5eqtri 2057 . 2  i^i  |^| (/)
72, 6syl6eq 2085 1  X  (/)  i^i  |^| X
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   _Vcvv 2551    i^i cin 2910   (/)c0 3218   |^|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-in1 544  ax-in2 545  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-dif 2914  df-in 2918  df-ss 2925  df-nul 3219  df-int 3607
This theorem is referenced by: (None)
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