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Theorem soeq1 4760
 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 4744 . . 3
2 breq 4394 . . . . 5
3 biidd 237 . . . . 5
4 breq 4394 . . . . 5
52, 3, 43orbi123d 1298 . . . 4
652ralbidv 2845 . . 3
71, 6anbi12d 709 . 2
8 df-so 4742 . 2
9 df-so 4742 . 2
107, 8, 93bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 367   w3o 971   wceq 1403  wral 2751   class class class wbr 4392   wpo 4739   wor 4740 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-ext 2378 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3or 973  df-ex 1632  df-cleq 2392  df-clel 2395  df-ral 2756  df-br 4393  df-po 4741  df-so 4742 This theorem is referenced by:  weeq1  4808  ltsopi  9214  cnso  14079  opsrtoslem2  18359  soeq12d  35309
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