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Theorem dfso3 25182
 Description: Expansion of the definition of a strict order. (Contributed by Scott Fenton, 6-Jun-2016.)
Assertion
Ref Expression
dfso3
Distinct variable groups:   ,,,   ,,,

Proof of Theorem dfso3
StepHypRef Expression
1 ne0i 3636 . . . . 5
2 r19.27zv 3729 . . . . 5
31, 2syl 16 . . . 4
43ralbiia 2739 . . 3
54ralbii 2731 . 2
6 df-3an 939 . . . 4
76ralbii 2731 . . 3
872ralbii 2733 . 2
9 df-po 4506 . . . 4
109anbi1i 678 . . 3
11 df-so 4507 . . 3
12 r19.26-2 2841 . . 3
1310, 11, 123bitr4i 270 . 2
145, 8, 133bitr4ri 271 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360   w3o 936   w3a 937   wcel 1726   wne 2601  wral 2707  c0 3630   class class class wbr 4215   wpo 4504   wor 4505 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-v 2960  df-dif 3325  df-nul 3631  df-po 4506  df-so 4507
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