MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  soeq1 Unicode version

Theorem soeq1 4824
Description: Equality theorem for the strict ordering predicate. (Contributed by NM, 16-Mar-1997.)
Assertion
Ref Expression
soeq1

Proof of Theorem soeq1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 poeq1 4808 . . 3
2 breq 4454 . . . . 5
3 biidd 237 . . . . 5
4 breq 4454 . . . . 5
52, 3, 43orbi123d 1298 . . . 4
652ralbidv 2901 . . 3
71, 6anbi12d 710 . 2
8 df-so 4806 . 2
9 df-so 4806 . 2
107, 8, 93bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  \/w3o 972  =wceq 1395  A.wral 2807   class class class wbr 4452  Powpo 4803  Orwor 4804
This theorem is referenced by:  weeq1  4872  ltsopi  9287  cnso  13980  opsrtoslem2  18149  soeq12d  30983
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-ex 1613  df-cleq 2449  df-clel 2452  df-ral 2812  df-br 4453  df-po 4805  df-so 4806
  Copyright terms: Public domain W3C validator