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Theorem soeq2 4081
 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 4079 . . . 4
2 soss 4079 . . . 4
31, 2anim12i 325 . . 3
4 eqss 2988 . . 3
5 dfbi2 374 . . 3
63, 4, 53imtr4i 194 . 2
76bicomd 133 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102   wceq 1259   wss 2945   wor 4060 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-in 2952  df-ss 2959  df-po 4061  df-iso 4062 This theorem is referenced by: (None)
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