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Theorem relbrcnv 5541
 Description: When 𝑅 is a relation, the sethood assumptions on brcnv 5337 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 5539 . 2 (Rel 𝑅 → (𝐴𝑅𝐵𝐵𝑅𝐴))
31, 2ax-mp 5 1 (𝐴𝑅𝐵𝐵𝑅𝐴)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196   class class class wbr 4685  ◡ccnv 5142  Rel wrel 5148 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-nul 4822  ax-pr 4936 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-eu 2502  df-mo 2503  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-rex 2947  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-br 4686  df-opab 4746  df-xp 5149  df-rel 5150  df-cnv 5151 This theorem is referenced by:  compssiso  9234  fneval  32472  brcnvep  34170  brid  34218  br1cnvxrn2  34294  br1cnvssrres  34395  brcnvssr  34396  brco2f1o  38647  brco3f1o  38648  neicvgnvor  38731
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