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Theorem caovdir 6402
 Description: Reverse distributive law. (Contributed by NM, 26-Aug-1995.)
Hypotheses
Ref Expression
caovdir.1
caovdir.2
caovdir.3
caovdir.com
caovdir.distr
Assertion
Ref Expression
caovdir
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovdir
StepHypRef Expression
1 caovdir.3 . . 3
2 caovdir.1 . . 3
3 caovdir.2 . . 3
4 caovdir.distr . . 3
51, 2, 3, 4caovdi 6387 . 2
6 ovex 6220 . . 3
7 caovdir.com . . 3
81, 6, 7caovcom 6365 . 2
91, 2, 7caovcom 6365 . . 3
101, 3, 7caovcom 6365 . . 3
119, 10oveq12i 6207 . 2
125, 8, 113eqtr3i 2489 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1370   wcel 1758  cvv 3072  (class class class)co 6195 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431  ax-nul 4524 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2265  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-ne 2647  df-ral 2801  df-rex 2802  df-rab 2805  df-v 3074  df-sbc 3289  df-dif 3434  df-un 3436  df-in 3438  df-ss 3445  df-nul 3741  df-if 3895  df-sn 3981  df-pr 3983  df-op 3987  df-uni 4195  df-br 4396  df-iota 5484  df-fv 5529  df-ov 6198 This theorem is referenced by:  caovdilem  6403  adderpqlem  9229  addassnq  9233  prlem934  9308  prlem936  9322  recexsrlem  9376  mulgt0sr  9378
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