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Theorem mincom 10576
Description: The minimum of two reals is commutative. (Contributed by Jim Kingdon, 8-Feb-2021.)
Assertion
Ref Expression
mincom  |- inf ( { A ,  B } ,  RR ,  <  )  = inf ( { B ,  A } ,  RR ,  <  )

Proof of Theorem mincom
StepHypRef Expression
1 prcom 3503 . 2  |-  { A ,  B }  =  { B ,  A }
21infeq1i 6655 1  |- inf ( { A ,  B } ,  RR ,  <  )  = inf ( { B ,  A } ,  RR ,  <  )
Colors of variables: wff set class
Syntax hints:    = wceq 1287   {cpr 3432  infcinf 6625   RRcr 7296    < clt 7469
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-rex 2361  df-rab 2364  df-v 2617  df-un 2992  df-pr 3438  df-uni 3639  df-sup 6626  df-inf 6627
This theorem is referenced by: (None)
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