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Theorem nmhmrcl2 21232
 Description: Reverse closure for a normed module homomorphism. (Contributed by Mario Carneiro, 18-Oct-2015.)
Assertion
Ref Expression
nmhmrcl2 NMHom NrmMod

Proof of Theorem nmhmrcl2
StepHypRef Expression
1 isnmhm 21230 . . 3 NMHom NrmMod NrmMod LMHom NGHom
21simplbi 460 . 2 NMHom NrmMod NrmMod
32simprd 463 1 NMHom NrmMod
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wcel 1804  (class class class)co 6281   LMHom clmhm 17643  NrmModcnlm 21078   NGHom cnghm 21190   NMHom cnmhm 21191 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-8 1806  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pow 4615  ax-pr 4676 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-eu 2272  df-mo 2273  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-sbc 3314  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-uni 4235  df-br 4438  df-opab 4496  df-id 4785  df-xp 4995  df-rel 4996  df-cnv 4997  df-co 4998  df-dm 4999  df-iota 5541  df-fun 5580  df-fv 5586  df-ov 6284  df-oprab 6285  df-mpt2 6286  df-nmhm 21194 This theorem is referenced by:  nmhmco  21240  nmhmplusg  21241
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