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Theorem disjimres 37558
Description: Disjointness condition for restriction. (Contributed by Peter Mazsa, 27-Sep-2021.)
Assertion
Ref Expression
disjimres ( Disj 𝑅 → Disj (𝑅𝐴))

Proof of Theorem disjimres
StepHypRef Expression
1 resss 6004 . 2 (𝑅𝐴) ⊆ 𝑅
21disjssi 37540 1 ( Disj 𝑅 → Disj (𝑅𝐴))
Colors of variables: wff setvar class
Syntax hints:  wi 4  cres 5677   Disj wdisjALTV 37015
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5298  ax-nul 5305  ax-pr 5426
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3063  df-rex 3072  df-rab 3434  df-v 3477  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4322  df-if 4528  df-sn 4628  df-pr 4630  df-op 4634  df-br 5148  df-opab 5210  df-id 5573  df-xp 5681  df-rel 5682  df-cnv 5683  df-co 5684  df-dm 5685  df-rn 5686  df-res 5687  df-coss 37219  df-cnvrefrel 37335  df-funALTV 37490  df-disjALTV 37513
This theorem is referenced by:  disjiminres  37560  disjimxrnres  37561  disjALTVidres  37564
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