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Theorem disjimres 36456
 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 5854 . 2 (𝑅𝐴) ⊆ 𝑅
21disjssi 36441 1 ( Disj 𝑅 → Disj (𝑅𝐴))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↾ cres 5531   Disj wdisjALTV 35963 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 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2730  ax-sep 5174  ax-nul 5181  ax-pr 5303 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-ral 3076  df-rex 3077  df-rab 3080  df-v 3412  df-dif 3864  df-un 3866  df-in 3868  df-ss 3878  df-nul 4229  df-if 4425  df-sn 4527  df-pr 4529  df-op 4533  df-br 5038  df-opab 5100  df-id 5435  df-xp 5535  df-rel 5536  df-cnv 5537  df-co 5538  df-dm 5539  df-rn 5540  df-res 5541  df-coss 36135  df-cnvrefrel 36241  df-funALTV 36391  df-disjALTV 36414 This theorem is referenced by:  disjiminres  36458  disjimxrnres  36459  disjALTVidres  36462
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