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Theorem caovord 6486
 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:   ,,,   ,,,   ,,,   ,,,   ,,,   ,S,,

Proof of Theorem caovord
StepHypRef Expression
1 oveq1 6303 . . . 4
2 oveq1 6303 . . . 4
31, 2breq12d 4465 . . 3
43bibi2d 318 . 2
5 caovord.1 . . 3
6 caovord.2 . . 3
7 breq1 4455 . . . . . 6
8 oveq2 6304 . . . . . . 7
98breq1d 4462 . . . . . 6
107, 9bibi12d 321 . . . . 5
11 breq2 4456 . . . . . 6
12 oveq2 6304 . . . . . . 7
1312breq2d 4464 . . . . . 6
1411, 13bibi12d 321 . . . . 5
1510, 14sylan9bb 699 . . . 4
1615imbi2d 316 . . 3
17 caovord.3 . . 3
185, 6, 16, 17vtocl2 3162 . 2
194, 18vtoclga 3173 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818   cvv 3109   class class class wbr 4452  (class class class)co 6296 This theorem is referenced by:  caovord2  6487  caovord3  6488  genpcl  9407 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-iota 5556  df-fv 5601  df-ov 6299
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