Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  maxcom Unicode version

Theorem maxcom 11080
 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

Proof of Theorem maxcom
StepHypRef Expression
1 prcom 3631 . 2
21supeq1i 6920 1
 Colors of variables: wff set class Syntax hints:   wceq 1332  cpr 3557  csup 6914  cr 7710   clt 7891 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-rab 2441  df-v 2711  df-un 3102  df-pr 3563  df-uni 3769  df-sup 6916 This theorem is referenced by:  maxle2  11089  maxclpr  11099  2zsupmax  11102  xrmaxiflemcom  11123
 Copyright terms: Public domain W3C validator