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Theorem disjimi 37641
Description: Every disjoint relation generates equivalent cosets by the relation, inference version. (Contributed by Peter Mazsa, 30-Sep-2021.)
Hypothesis
Ref Expression
disjimi.1 Disj 𝑅
Assertion
Ref Expression
disjimi EqvRel ≀ 𝑅

Proof of Theorem disjimi
StepHypRef Expression
1 disjimi.1 . 2 Disj 𝑅
2 disjim 37640 . 2 ( Disj 𝑅 → EqvRel ≀ 𝑅)
31, 2ax-mp 5 1 EqvRel ≀ 𝑅
Colors of variables: wff setvar class
Syntax hints:  ccoss 37032   EqvRel weqvrel 37049   Disj wdisjALTV 37066
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 5299  ax-nul 5306  ax-pr 5427
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-mo 2535  df-eu 2564  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-ral 3063  df-rex 3072  df-rab 3434  df-v 3477  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-br 5149  df-opab 5211  df-id 5574  df-xp 5682  df-rel 5683  df-cnv 5684  df-co 5685  df-dm 5686  df-rn 5687  df-res 5688  df-coss 37270  df-refrel 37371  df-cnvrefrel 37386  df-symrel 37403  df-trrel 37433  df-eqvrel 37444  df-disjALTV 37564
This theorem is referenced by:  eqvrel0  37645  eqvrelcoss0  37647  eqvrelid  37648  eqvrel1cossidres  37649  eqvrel1cossinidres  37650  eqvrel1cossxrnidres  37651  eqvrelcossid  37653
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