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Theorem relbrcnv 5157
Description: When  R is a relation, the sethood assumptions on brcnv 4967 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 5155 . 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 176   class class class wbr 4125   `'ccnv 4791   Rel wrel 4797
This theorem is referenced by:  compssiso  8147  ballotlemimin  24332  fneval  25879
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-14 1719  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347  ax-sep 4243  ax-nul 4251  ax-pr 4316
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 937  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-eu 2221  df-mo 2222  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-ne 2531  df-ral 2633  df-rex 2634  df-rab 2637  df-v 2875  df-dif 3241  df-un 3243  df-in 3245  df-ss 3252  df-nul 3544  df-if 3655  df-sn 3735  df-pr 3736  df-op 3738  df-br 4126  df-opab 4180  df-xp 4798  df-rel 4799  df-cnv 4800
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