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Theorem cosscnvelrels 35182
 Description: Cosets of converse sets are elements of the relations class. (Contributed by Peter Mazsa, 31-Aug-2021.)
Assertion
Ref Expression
cosscnvelrels (𝐴𝑉 → ≀ 𝐴 ∈ Rels )

Proof of Theorem cosscnvelrels
StepHypRef Expression
1 cnvelrels 35180 . 2 (𝐴𝑉𝐴 ∈ Rels )
2 cosselrels 35181 . 2 (𝐴 ∈ Rels → ≀ 𝐴 ∈ Rels )
31, 2syl 17 1 (𝐴𝑉 → ≀ 𝐴 ∈ Rels )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2050  ◡ccnv 5400   ≀ ccoss 34897   Rels crels 34899 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-13 2301  ax-ext 2744  ax-sep 5054  ax-nul 5061  ax-pow 5113  ax-pr 5180  ax-un 7273 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-mo 2547  df-eu 2584  df-clab 2753  df-cleq 2765  df-clel 2840  df-nfc 2912  df-ral 3087  df-rex 3088  df-rab 3091  df-v 3411  df-dif 3826  df-un 3828  df-in 3830  df-ss 3837  df-nul 4173  df-if 4345  df-pw 4418  df-sn 4436  df-pr 4438  df-op 4442  df-uni 4707  df-br 4924  df-opab 4986  df-xp 5407  df-rel 5408  df-cnv 5409  df-co 5410  df-dm 5411  df-rn 5412  df-coss 35104  df-rels 35170 This theorem is referenced by:  dfdisjs2  35387  eldisjs2  35401
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