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Theorem caovord 6499
 Description: Convert an operation ordering law to class notation. (Contributed by NM, 19-Feb-1996.)
Hypotheses
Ref Expression
caovord.1
caovord.2
caovord.3
Assertion
Ref Expression
caovord
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovord
StepHypRef Expression
1 oveq1 6315 . . . 4
2 oveq1 6315 . . . 4
31, 2breq12d 4408 . . 3
43bibi2d 325 . 2
5 caovord.1 . . 3
6 caovord.2 . . 3
7 breq1 4398 . . . . . 6
8 oveq2 6316 . . . . . . 7
98breq1d 4405 . . . . . 6
107, 9bibi12d 328 . . . . 5
11 breq2 4399 . . . . . 6
12 oveq2 6316 . . . . . . 7
1312breq2d 4407 . . . . . 6
1411, 13bibi12d 328 . . . . 5
1510, 14sylan9bb 714 . . . 4
1615imbi2d 323 . . 3
17 caovord.3 . . 3
185, 6, 16, 17vtocl2 3088 . 2
194, 18vtoclga 3099 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376   wceq 1452   wcel 1904  cvv 3031   class class class wbr 4395  (class class class)co 6308 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-iota 5553  df-fv 5597  df-ov 6311 This theorem is referenced by:  caovord2  6500  caovord3  6501  genpcl  9451
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