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Theorem relbrcnv 5751
 Description: When 𝑅 is a relation, the sethood assumptions on brcnv 5541 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 5749 . 2 (Rel 𝑅 → (𝐴𝑅𝐵𝐵𝑅𝐴))
31, 2ax-mp 5 1 (𝐴𝑅𝐵𝐵𝑅𝐴)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 198   class class class wbr 4875  ◡ccnv 5345  Rel wrel 5351 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803  ax-sep 5007  ax-nul 5015  ax-pr 5129 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-3an 1113  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-mo 2605  df-eu 2640  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ral 3122  df-rex 3123  df-rab 3126  df-v 3416  df-dif 3801  df-un 3803  df-in 3805  df-ss 3812  df-nul 4147  df-if 4309  df-sn 4400  df-pr 4402  df-op 4406  df-br 4876  df-opab 4938  df-xp 5352  df-rel 5353  df-cnv 5354 This theorem is referenced by:  compssiso  9518  fneval  32880  brcnvep  34578  brid  34621  brcnvrabga  34653  br1cnvxrn2  34697  br1cnvssrres  34798  brcnvssr  34799  brco2f1o  39165  brco3f1o  39166  neicvgnvor  39249
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