Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  caovord3d Structured version   Unicode version

Theorem caovord3d 6250
 Description: Ordering law. (Contributed by Mario Carneiro, 30-Dec-2014.)
Hypotheses
Ref Expression
caovordg.1
caovordd.2
caovordd.3
caovordd.4
caovord2d.com
caovord3d.5
Assertion
Ref Expression
caovord3d
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovord3d
StepHypRef Expression
1 breq1 4208 . 2
2 caovordg.1 . . . 4
3 caovordd.2 . . . 4
4 caovordd.4 . . . 4
5 caovordd.3 . . . 4
6 caovord2d.com . . . 4
72, 3, 4, 5, 6caovord2d 6249 . . 3
8 caovord3d.5 . . . 4
92, 8, 5, 4caovordd 6248 . . 3
107, 9bibi12d 313 . 2
111, 10syl5ibr 213 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725   class class class wbr 4205  (class class class)co 6074 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2703  df-rex 2704  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-uni 4009  df-br 4206  df-iota 5411  df-fv 5455  df-ov 6077
 Copyright terms: Public domain W3C validator