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Theorem reldmnmhm 18747
Description: Lemma for module homomorphisms. (Contributed by Mario Carneiro, 18-Oct-2015.)
Assertion
Ref Expression
reldmnmhm  |-  Rel  dom NMHom

Proof of Theorem reldmnmhm
Dummy variables  s 
t are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-nmhm 18744 . 2  |- NMHom  =  ( s  e. NrmMod ,  t  e. NrmMod  |->  ( ( s LMHom  t
)  i^i  ( s NGHom  t ) ) )
21reldmmpt2 6181 1  |-  Rel  dom NMHom
Colors of variables: wff set class
Syntax hints:    i^i cin 3319   dom cdm 4878   Rel wrel 4883  (class class class)co 6081   LMHom clmhm 16095  NrmModcnlm 18628   NGHom cnghm 18740   NMHom cnmhm 18741
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885  df-dm 4888  df-oprab 6085  df-mpt2 6086  df-nmhm 18744
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