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Theorem caovcanrd 5606
Description: Commute the arguments of an operation cancellation law. (Contributed by Mario Carneiro, 30-Dec-2014.)
Hypotheses
Ref Expression
caovcang.1  T  S  S  F  F
caovcand.2  T
caovcand.3  S
caovcand.4  C  S
caovcanrd.5  S
caovcanrd.6  S  S  F  F
Assertion
Ref Expression
caovcanrd  F  C F  C
Distinct variable groups:   ,,,   ,,,   , C,,   ,,,   , F,,   , S,,   , T,,

Proof of Theorem caovcanrd
StepHypRef Expression
1 caovcanrd.6 . . . 4  S  S  F  F
2 caovcanrd.5 . . . 4  S
3 caovcand.3 . . . 4  S
41, 2, 3caovcomd 5599 . . 3  F  F
5 caovcand.4 . . . 4  C  S
61, 2, 5caovcomd 5599 . . 3  F C  C F
74, 6eqeq12d 2051 . 2  F  F C  F  C F
8 caovcang.1 . . 3  T  S  S  F  F
9 caovcand.2 . . 3  T
108, 9, 3, 5caovcand 5605 . 2  F  F C  C
117, 10bitr3d 179 1  F  C F  C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   w3a 884   wceq 1242   wcel 1390  (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-bnd 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: (None)
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