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Theorem maxcom 10926
Description: The maximum of two reals is commutative. Lemma 3.9 of [Geuvers], p. 10. (Contributed by Jim Kingdon, 21-Dec-2021.)
Assertion
Ref Expression
maxcom  |-  sup ( { A ,  B } ,  RR ,  <  )  =  sup ( { B ,  A } ,  RR ,  <  )

Proof of Theorem maxcom
StepHypRef Expression
1 prcom 3567 . 2  |-  { A ,  B }  =  { B ,  A }
21supeq1i 6841 1  |-  sup ( { A ,  B } ,  RR ,  <  )  =  sup ( { B ,  A } ,  RR ,  <  )
Colors of variables: wff set class
Syntax hints:    = wceq 1314   {cpr 3496   supcsup 6835   RRcr 7583    < clt 7764
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rex 2397  df-rab 2400  df-v 2660  df-un 3043  df-pr 3502  df-uni 3705  df-sup 6837
This theorem is referenced by:  maxle2  10935  maxclpr  10945  2zsupmax  10948  xrmaxiflemcom  10969
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