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Theorem reldmnmhm 18620
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 18617 . 2  |- NMHom  =  ( s  e. NrmMod ,  t  e. NrmMod  |->  ( ( s LMHom  t
)  i^i  ( s NGHom  t ) ) )
21reldmmpt2 6122 1  |-  Rel  dom NMHom
Colors of variables: wff set class
Syntax hints:    i^i cin 3264   dom cdm 4820   Rel wrel 4825  (class class class)co 6022   LMHom clmhm 16024  NrmModcnlm 18501   NGHom cnghm 18613   NMHom cnmhm 18614
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 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370  ax-sep 4273  ax-nul 4281  ax-pr 4346
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 2244  df-mo 2245  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-ne 2554  df-ral 2656  df-rex 2657  df-rab 2660  df-v 2903  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-nul 3574  df-if 3685  df-sn 3765  df-pr 3766  df-op 3768  df-br 4156  df-opab 4210  df-xp 4826  df-rel 4827  df-dm 4830  df-oprab 6026  df-mpt2 6027  df-nmhm 18617
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