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Theorem caovord2 6472
 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 6471 . 2
5 caovord2.3 . . . 4
6 caovord2.com . . . 4
75, 1, 6caovcom 6457 . . 3
85, 2, 6caovcom 6457 . . 3
97, 8breq12i 4446 . 2
104, 9syl6bb 261 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1383   wcel 1804  cvv 3095   class class class wbr 4437  (class class class)co 6281 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-uni 4235  df-br 4438  df-iota 5541  df-fv 5586  df-ov 6284 This theorem is referenced by:  caovord3  6473  genpnmax  9388  addclprlem1  9397  mulclprlem  9400  distrlem4pr  9407  ltexprlem6  9422  reclem3pr  9430  ltsosr  9474
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