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Theorem eqvrel1cossxrnidres 37568
Description: The cosets by a range Cartesian product with a restricted identity relation are in equivalence relation. (Contributed by Peter Mazsa, 31-Dec-2021.)
Assertion
Ref Expression
eqvrel1cossxrnidres EqvRel ≀ (𝑅 ⋉ ( I ↾ 𝐴))

Proof of Theorem eqvrel1cossxrnidres
StepHypRef Expression
1 disjALTVxrnidres 37534 . 2 Disj (𝑅 ⋉ ( I ↾ 𝐴))
21disjimi 37558 1 EqvRel ≀ (𝑅 ⋉ ( I ↾ 𝐴))
Colors of variables: wff setvar class
Syntax hints:   I cid 5569  cres 5674  cxrn 36948  ccoss 36949   EqvRel weqvrel 36966
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 5295  ax-nul 5302  ax-pr 5423  ax-un 7712
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-ne 2942  df-ral 3063  df-rex 3072  df-rab 3434  df-v 3477  df-dif 3949  df-un 3951  df-in 3953  df-ss 3963  df-nul 4321  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4905  df-br 5145  df-opab 5207  df-mpt 5228  df-id 5570  df-xp 5678  df-rel 5679  df-cnv 5680  df-co 5681  df-dm 5682  df-rn 5683  df-res 5684  df-ima 5685  df-iota 6487  df-fun 6537  df-fn 6538  df-f 6539  df-fo 6541  df-fv 6543  df-1st 7962  df-2nd 7963  df-ec 8693  df-xrn 37147  df-coss 37187  df-refrel 37288  df-cnvrefrel 37303  df-symrel 37320  df-trrel 37350  df-eqvrel 37361  df-funALTV 37458  df-disjALTV 37481
This theorem is referenced by: (None)
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