Hilbert Space Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HSE Home  >  Th. List  >  cmbri Unicode version

Theorem cmbri 23045
 Description: Binary relation expressing the commutes relation. Definition of commutes in [Kalmbach] p. 20. (Contributed by NM, 6-Aug-2004.) (New usage is discouraged.)
Hypotheses
Ref Expression
pjoml2.1
pjoml2.2
Assertion
Ref Expression
cmbri

Proof of Theorem cmbri
StepHypRef Expression
1 pjoml2.1 . 2
2 pjoml2.2 . 2
3 cmbr 23039 . 2
41, 2, 3mp2an 654 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1649   wcel 1721   cin 3279   class class class wbr 4172  cfv 5413  (class class class)co 6040  cch 22385  cort 22386   chj 22389   ccm 22392 This theorem is referenced by:  cmcmlem  23046  cmcm2i  23048  cmbr2i  23051  cmbr3i  23055  pjclem1  23651  pjci  23656 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-nul 4298  ax-pr 4363 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-opab 4227  df-iota 5377  df-fv 5421  df-ov 6043  df-cm 23038
 Copyright terms: Public domain W3C validator