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Theorem pr01ssre 26614
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 9492 . 2  |-  0  e.  RR
2 1re 9491 . 2  |-  1  e.  RR
3 prssi 4132 . 2  |-  ( ( 0  e.  RR  /\  1  e.  RR )  ->  { 0 ,  1 }  C_  RR )
41, 2, 3mp2an 672 1  |-  { 0 ,  1 }  C_  RR
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1758    C_ wss 3431   {cpr 3982   RRcr 9387   0cc0 9388   1c1 9389
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431  ax-1cn 9446  ax-icn 9447  ax-addcl 9448  ax-addrcl 9449  ax-mulcl 9450  ax-mulrcl 9451  ax-i2m1 9456  ax-1ne0 9457  ax-rnegex 9459  ax-rrecex 9460  ax-cnre 9461
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-ne 2647  df-ral 2801  df-rex 2802  df-rab 2805  df-v 3074  df-dif 3434  df-un 3436  df-in 3438  df-ss 3445  df-nul 3741  df-if 3895  df-sn 3981  df-pr 3983  df-op 3987  df-uni 4195  df-br 4396  df-iota 5484  df-fv 5529  df-ov 6198
This theorem is referenced by:  indsum  26619
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