Theorem mincom 11000

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

Step	Hyp	Ref	Expression
1		prcom 3599	. 2 |- { A , B } = { B , A }
2	1	infeq1i 6900	1 |- inf ( { A , B } , RR , < ) = inf ( { B , A } , RR , < )

Syntax hints:   = wceq 1331   {cpr 3528  infcinf 6870   RRcr 7619   < clt 7800

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-rab 2425  df-v 2688  df-un 3075  df-pr 3534  df-uni 3737  df-sup 6871  df-inf 6872

This theorem is referenced by: (None)