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Theorem caovord3d 5941
 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 3932 . 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 5940 . . 3
8 caovord3d.5 . . . 4
92, 8, 5, 4caovordd 5939 . . 3
107, 9bibi12d 234 . 2
111, 10syl5ibr 155 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   w3a 962   wceq 1331   wcel 1480   class class class wbr 3929  (class class class)co 5774 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131  df-ov 5777 This theorem is referenced by:  ordpipqqs  7189  ltsrprg  7562
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