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Theorem relbrcnv 5212
Description: When  R is a relation, the sethood assumptions on brcnv 5022 can be omitted. (Contributed by Mario Carneiro, 28-Apr-2015.)
Hypothesis
Ref Expression
relbrcnv.1  |-  Rel  R
Assertion
Ref Expression
relbrcnv  |-  ( A `' R B  <->  B R A )

Proof of Theorem relbrcnv
StepHypRef Expression
1 relbrcnv.1 . 2  |-  Rel  R
2 relbrcnvg 5210 . 2  |-  ( Rel 
R  ->  ( A `' R B  <->  B R A ) )
31, 2ax-mp 8 1  |-  ( A `' R B  <->  B R A )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   class class class wbr 4180   `'ccnv 4844   Rel wrel 4850
This theorem is referenced by:  compssiso  8218  ballotlemimin  24724  fneval  26265
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393  ax-sep 4298  ax-nul 4306  ax-pr 4371
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2266  df-mo 2267  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ne 2577  df-ral 2679  df-rex 2680  df-rab 2683  df-v 2926  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-br 4181  df-opab 4235  df-xp 4851  df-rel 4852  df-cnv 4853
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