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Theorem soeq2 4825
Description: Equality theorem for the strict ordering predicate. (Contributed by NM, 16-Mar-1997.)
Assertion
Ref Expression
soeq2

Proof of Theorem soeq2
StepHypRef Expression
1 soss 4823 . . . 4
2 soss 4823 . . . 4
31, 2anim12i 566 . . 3
4 eqss 3518 . . 3
5 dfbi2 628 . . 3
63, 4, 53imtr4i 266 . 2
76bicomd 201 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  C_wss 3475  Orwor 4804
This theorem is referenced by:  weeq2  4873  wemapso2  8000  oemapso  8122  fin2i  8696  isfin2-2  8720  fin1a2lem10  8810  zorn2lem7  8903  zornn0g  8906  opsrtoslem2  18149  sltsolem1  29428  soeq12d  30983  aomclem1  31000
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-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-in 3482  df-ss 3489  df-po 4805  df-so 4806
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