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Theorem ismri2dd 13864
 Description: Definition of independence of a subset of the base set in a Moore system. One-way deduction form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
ismri2.1 mrCls
ismri2.2 mrInd
ismri2d.3 Moore
ismri2d.4
ismri2dd.5
Assertion
Ref Expression
ismri2dd
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem ismri2dd
StepHypRef Expression
1 ismri2dd.5 . 2
2 ismri2.1 . . 3 mrCls
3 ismri2.2 . . 3 mrInd
4 ismri2d.3 . . 3 Moore
5 ismri2d.4 . . 3
62, 3, 4, 5ismri2d 13863 . 2
71, 6mpbird 225 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1653   wcel 1726  wral 2707   cdif 3319   wss 3322  csn 3816  cfv 5457  Moorecmre 13812  mrClscmrc 13813  mrIndcmri 13814 This theorem is referenced by:  mrissmrid  13871  mreexmrid  13873  acsfiindd  14608 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-13 1728  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-pow 4380  ax-pr 4406  ax-un 4704 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-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-iota 5421  df-fun 5459  df-fv 5465  df-mre 13816  df-mri 13818
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