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Theorem caovord2 6251
 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 6250 . 2
5 caovord2.3 . . . 4
6 caovord2.com . . . 4
75, 1, 6caovcom 6236 . . 3
85, 2, 6caovcom 6236 . . 3
97, 8breq12i 4213 . 2
104, 9syl6bb 253 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  cvv 2948   class class class wbr 4204  (class class class)co 6073 This theorem is referenced by:  caovord3  6252  genpnmax  8876  addclprlem1  8885  mulclprlem  8888  distrlem4pr  8895  ltexprlem6  8910  reclem3pr  8918  ltsosr  8961 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-ral 2702  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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