Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  caovord2d Structured version   Unicode version

Theorem caovord2d 6259
 Description: Operation ordering law with commuted arguments. (Contributed by Mario Carneiro, 30-Dec-2014.)
Hypotheses
Ref Expression
caovordg.1
caovordd.2
caovordd.3
caovordd.4
caovord2d.com
Assertion
Ref Expression
caovord2d
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovord2d
StepHypRef Expression
1 caovordg.1 . . 3
2 caovordd.2 . . 3
3 caovordd.3 . . 3
4 caovordd.4 . . 3
51, 2, 3, 4caovordd 6258 . 2
6 caovord2d.com . . . 4
76, 4, 2caovcomd 6246 . . 3
86, 4, 3caovcomd 6246 . . 3
97, 8breq12d 4228 . 2
105, 9bitrd 246 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726   class class class wbr 4215  (class class class)co 6084 This theorem is referenced by:  caovord3d  6260 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-ov 6087
 Copyright terms: Public domain W3C validator