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Theorem caovord 6250
 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 6080 . . . 4
2 oveq1 6080 . . . 4
31, 2breq12d 4217 . . 3
43bibi2d 310 . 2
5 caovord.1 . . 3
6 caovord.2 . . 3
7 breq1 4207 . . . . . 6
8 oveq2 6081 . . . . . . 7
98breq1d 4214 . . . . . 6
107, 9bibi12d 313 . . . . 5
11 breq2 4208 . . . . . 6
12 oveq2 6081 . . . . . . 7
1312breq2d 4216 . . . . . 6
1411, 13bibi12d 313 . . . . 5
1510, 14sylan9bb 681 . . . 4
1615imbi2d 308 . . 3
17 caovord.3 . . 3
185, 6, 16, 17vtocl2 2999 . 2
194, 18vtoclga 3009 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  cvv 2948   class class class wbr 4204  (class class class)co 6073 This theorem is referenced by:  caovord2  6251  caovord3  6252  genpcl  8877 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-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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