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Theorem relbrcnv 6063
Description: When 𝑅 is a relation, the sethood assumptions on brcnv 5842 can be omitted. (Contributed by Mario Carneiro, 28-Apr-2015.)
Hypothesis
Ref Expression
relbrcnv.1 Rel 𝑅
Assertion
Ref Expression
relbrcnv (𝐴𝑅𝐵𝐵𝑅𝐴)

Proof of Theorem relbrcnv
StepHypRef Expression
1 relbrcnv.1 . 2 Rel 𝑅
2 relbrcnvg 6061 . 2 (Rel 𝑅 → (𝐴𝑅𝐵𝐵𝑅𝐴))
31, 2ax-mp 5 1 (𝐴𝑅𝐵𝐵𝑅𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 205   class class class wbr 5109  ccnv 5636  Rel wrel 5642
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-ext 2704  ax-sep 5260  ax-nul 5267  ax-pr 5388
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-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-rex 3071  df-rab 3407  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4287  df-if 4491  df-sn 4591  df-pr 4593  df-op 4597  df-br 5110  df-opab 5172  df-xp 5643  df-rel 5644  df-cnv 5645
This theorem is referenced by:  compssiso  10318  fneval  34877  br1cnvinxp  36766  brcnvep  36775  brid  36817  brcnvrabga  36853  br1cnvxrn2  36908  br1cnvssrres  37017  brcnvssr  37018  brco2f1o  42396  brco3f1o  42397  neicvgnvor  42480
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