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Theorem cosscnvex 37196
Description: If 𝐴 is a set then the class of cosets by the converse of 𝐴 is a set. (Contributed by Peter Mazsa, 18-Oct-2019.)
Assertion
Ref Expression
cosscnvex (𝐴𝑉 → ≀ 𝐴 ∈ V)

Proof of Theorem cosscnvex
StepHypRef Expression
1 cnvexg 7902 . 2 (𝐴𝑉𝐴 ∈ V)
2 cossex 37195 . 2 (𝐴 ∈ V → ≀ 𝐴 ∈ V)
31, 2syl 17 1 (𝐴𝑉 → ≀ 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Vcvv 3475  ccnv 5671  ccoss 36949
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-12 2172  ax-ext 2704  ax-sep 5295  ax-nul 5302  ax-pow 5359  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-clab 2711  df-cleq 2725  df-clel 2811  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-pw 4600  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4905  df-br 5145  df-opab 5207  df-xp 5678  df-rel 5679  df-cnv 5680  df-co 5681  df-dm 5682  df-rn 5683  df-coss 37187
This theorem is referenced by:  eldisjsdisj  37503
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