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Theorem caovdi 6268
 Description: Convert an operation distributive law to class notation. (Contributed by NM, 25-Aug-1995.) (Revised by Mario Carneiro, 28-Jun-2013.)
Hypotheses
Ref Expression
caovdi.1
caovdi.2
caovdi.3
caovdi.4
Assertion
Ref Expression
caovdi
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovdi
StepHypRef Expression
1 caovdi.1 . 2
2 caovdi.2 . 2
3 caovdi.3 . 2
4 tru 1331 . . 3
5 caovdi.4 . . . . 5
65a1i 11 . . . 4
76caovdig 6263 . . 3
84, 7mpan 653 . 2
91, 2, 3, 8mp3an 1280 1
 Colors of variables: wff set class Syntax hints:   wa 360   w3a 937   wtru 1326   wceq 1653   wcel 1726  cvv 2958  (class class class)co 6083 This theorem is referenced by:  caovdir  6283  caovlem2  6285 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ov 6086
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