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Theorem pr01ssre 28247
Description: The range of the indicator function is a subset of 
RR. (Contributed by Thierry Arnoux, 14-Aug-2017.)
Assertion
Ref Expression
pr01ssre  |-  { 0 ,  1 }  C_  RR

Proof of Theorem pr01ssre
StepHypRef Expression
1 0re 9585 . 2  |-  0  e.  RR
2 1re 9584 . 2  |-  1  e.  RR
3 prssi 4172 . 2  |-  ( ( 0  e.  RR  /\  1  e.  RR )  ->  { 0 ,  1 }  C_  RR )
41, 2, 3mp2an 670 1  |-  { 0 ,  1 }  C_  RR
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1823    C_ wss 3461   {cpr 4018   RRcr 9480   0cc0 9481   1c1 9482
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432  ax-1cn 9539  ax-icn 9540  ax-addcl 9541  ax-addrcl 9542  ax-mulcl 9543  ax-mulrcl 9544  ax-i2m1 9549  ax-1ne0 9550  ax-rnegex 9552  ax-rrecex 9553  ax-cnre 9554
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2651  df-ral 2809  df-rex 2810  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-sn 4017  df-pr 4019  df-op 4023  df-uni 4236  df-br 4440  df-iota 5534  df-fv 5578  df-ov 6273
This theorem is referenced by:  indsum  28252
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