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Theorem caovord2 5983
 Description: Operation ordering law with commuted arguments. (Contributed by NM, 27-Feb-1996.)
Hypotheses
Ref Expression
caovord.1
caovord.2
caovord.3
caovord2.3
caovord2.com
Assertion
Ref Expression
caovord2
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovord2
StepHypRef Expression
1 caovord.1 . . 3
2 caovord.2 . . 3
3 caovord.3 . . 3
41, 2, 3caovord 5982 . 2
5 caovord2.3 . . . 4
6 caovord2.com . . . 4
75, 1, 6caovcom 5968 . . 3
85, 2, 6caovcom 5968 . . 3
97, 8breq12i 3970 . 2
104, 9bitrdi 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1332   wcel 2125  cvv 2709   class class class wbr 3961  (class class class)co 5814 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-v 2711  df-un 3102  df-sn 3562  df-pr 3563  df-op 3565  df-uni 3769  df-br 3962  df-iota 5128  df-fv 5171  df-ov 5817 This theorem is referenced by:  caovord3  5984
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