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Theorem caovcanrd 6242
 Description: Commute the arguments of an operation cancellation law. (Contributed by Mario Carneiro, 30-Dec-2014.)
Hypotheses
Ref Expression
caovcang.1
caovcand.2
caovcand.3
caovcand.4
caovcanrd.5
caovcanrd.6
Assertion
Ref Expression
caovcanrd
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovcanrd
StepHypRef Expression
1 caovcanrd.6 . . . 4
2 caovcanrd.5 . . . 4
3 caovcand.3 . . . 4
41, 2, 3caovcomd 6235 . . 3
5 caovcand.4 . . . 4
61, 2, 5caovcomd 6235 . . 3
74, 6eqeq12d 2449 . 2
8 caovcang.1 . . 3
9 caovcand.2 . . 3
108, 9, 3, 5caovcand 6241 . 2
117, 10bitr3d 247 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  (class class class)co 6073 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076
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