Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  reldmlmhm Structured version   Unicode version

Theorem reldmlmhm 16106
 Description: Lemma for module homomorphisms. (Contributed by Stefan O'Rear, 31-Dec-2014.)
Assertion
Ref Expression
reldmlmhm LMHom

Proof of Theorem reldmlmhm
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-lmhm 16103 . 2 LMHom Scalar Scalar
21reldmmpt2 6184 1 LMHom
 Colors of variables: wff set class Syntax hints:   wa 360   wceq 1653  wral 2707  crab 2711  wsbc 3163   cdm 4881   wrel 4886  cfv 5457  (class class class)co 6084  cbs 13474  Scalarcsca 13537  cvsca 13538   cghm 15008  clmod 15955   LMHom clmhm 16100 This theorem is referenced by:  mendbas  27482 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-xp 4887  df-rel 4888  df-dm 4891  df-oprab 6088  df-mpt2 6089  df-lmhm 16103
 Copyright terms: Public domain W3C validator