Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  soeq2 Structured version   Unicode version

Theorem soeq2 4523
 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 4521 . . . 4
2 soss 4521 . . . 4
31, 2anim12i 550 . . 3
4 eqss 3363 . . 3
5 dfbi2 610 . . 3
63, 4, 53imtr4i 258 . 2
76bicomd 193 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wss 3320   wor 4502 This theorem is referenced by:  weeq2  4571  oemapso  7638  fin2i  8175  isfin2-2  8199  fin1a2lem10  8289  zorn2lem7  8382  zornn0g  8385  opsrtoslem2  16545  sltsolem1  25623  soeq12d  27112  aomclem1  27129 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-in 3327  df-ss 3334  df-po 4503  df-so 4504
 Copyright terms: Public domain W3C validator