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Theorem caovord2 5615
Description: Operation ordering law with commuted arguments. (Contributed by NM, 27-Feb-1996.)
Hypotheses
Ref Expression
caovord.1  _V
caovord.2  _V
caovord.3  S  R  F R F
caovord2.3  C 
_V
caovord2.com  F  F
Assertion
Ref Expression
caovord2  C  S  R  F C R F C
Distinct variable groups:   ,,,   ,,,   , C,,   , F,,   , R,,   , S,,

Proof of Theorem caovord2
StepHypRef Expression
1 caovord.1 . . 3  _V
2 caovord.2 . . 3  _V
3 caovord.3 . . 3  S  R  F R F
41, 2, 3caovord 5614 . 2  C  S  R  C F R C F
5 caovord2.3 . . . 4  C 
_V
6 caovord2.com . . . 4  F  F
75, 1, 6caovcom 5600 . . 3  C F  F C
85, 2, 6caovcom 5600 . . 3  C F  F C
97, 8breq12i 3764 . 2  C F R C F  F C R F C
104, 9syl6bb 185 1  C  S  R  F C R F C
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   wceq 1242   wcel 1390   _Vcvv 2551   class class class wbr 3755  (class class class)co 5455
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458
This theorem is referenced by:  caovord3  5616
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