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

Theorem cmbri 22017
 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 22011 . 2
41, 2, 3mp2an 656 1
 Colors of variables: wff set class Syntax hints:   wb 178   wceq 1619   wcel 1621   cin 3077   class class class wbr 3920  cfv 4592  (class class class)co 5710  cch 21339  cort 21340   chj 21343   ccm 21346 This theorem is referenced by:  cmcmlem  22018  cmcm2i  22020  cmbr2i  22023  cmbr3i  22027  pjclem1  22605  pjci  22610 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-rex 2514  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-uni 3728  df-br 3921  df-opab 3975  df-xp 4594  df-cnv 4596  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601  df-fv 4608  df-ov 5713  df-cm 22010
 Copyright terms: Public domain W3C validator