Mathbox for Stefan O'Rear < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  soeq12d Structured version   Unicode version

Theorem soeq12d 27103
 Description: Equality deduction for total orderings. (Contributed by Stefan O'Rear, 19-Jan-2015.)
Hypotheses
Ref Expression
weeq12d.l
weeq12d.r
Assertion
Ref Expression
soeq12d

Proof of Theorem soeq12d
StepHypRef Expression
1 weeq12d.l . . 3
2 soeq1 4514 . . 3
31, 2syl 16 . 2
4 weeq12d.r . . 3
5 soeq2 4515 . . 3
64, 5syl 16 . 2
73, 6bitrd 245 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wor 4494 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-3or 937  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-in 3319  df-ss 3326  df-br 4205  df-po 4495  df-so 4496
 Copyright terms: Public domain W3C validator