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Theorem soeq2 4732
 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 4730 . . . 4
2 soss 4730 . . . 4
31, 2anim12i 568 . . 3
4 eqss 3417 . . 3
5 dfbi2 632 . . 3
63, 4, 53imtr4i 269 . 2
76bicomd 204 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437   wss 3374   wor 4711 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2058  ax-ext 2403 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2410  df-cleq 2416  df-clel 2419  df-ral 2714  df-in 3381  df-ss 3388  df-po 4712  df-so 4713 This theorem is referenced by:  weeq2  4780  wemapso2  8016  oemapso  8134  fin2i  8671  isfin2-2  8695  fin1a2lem10  8785  zorn2lem7  8878  zornn0g  8881  opsrtoslem2  18646  sltsolem1  30501  soeq12d  35809  aomclem1  35825
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