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Theorem cosscnvelrels 36602
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 36600 . 2 (𝐴𝑉𝐴 ∈ Rels )
2 cosselrels 36601 . 2 (𝐴 ∈ Rels → ≀ 𝐴 ∈ Rels )
31, 2syl 17 1 (𝐴𝑉 → ≀ 𝐴 ∈ Rels )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  ccnv 5585  ccoss 36320   Rels crels 36322
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-12 2171  ax-ext 2709  ax-sep 5223  ax-nul 5230  ax-pow 5288  ax-pr 5352  ax-un 7580
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-ral 3069  df-rex 3070  df-rab 3073  df-v 3433  df-dif 3891  df-un 3893  df-in 3895  df-ss 3905  df-nul 4259  df-if 4462  df-pw 4537  df-sn 4564  df-pr 4566  df-op 4570  df-uni 4842  df-br 5076  df-opab 5138  df-xp 5592  df-rel 5593  df-cnv 5594  df-co 5595  df-dm 5596  df-rn 5597  df-coss 36524  df-rels 36590
This theorem is referenced by:  dfdisjs2  36807  eldisjs2  36821
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