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Theorem soeq1 4514
 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 4498 . . 3
2 breq 4206 . . . . 5
3 biidd 229 . . . . 5
4 breq 4206 . . . . 5
52, 3, 43orbi123d 1253 . . . 4
652ralbidv 2739 . . 3
71, 6anbi12d 692 . 2
8 df-so 4496 . 2
9 df-so 4496 . 2
107, 8, 93bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3o 935   wceq 1652  wral 2697   class class class wbr 4204   wpo 4493   wor 4494 This theorem is referenced by:  weeq1  4562  ltsopi  8757  cnso  12838  opsrtoslem2  16537  soeq12d  27093 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-11 1761  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-ex 1551  df-nf 1554  df-cleq 2428  df-clel 2431  df-ral 2702  df-br 4205  df-po 4495  df-so 4496
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