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Theorem isso2i 4538
 Description: Deduce strict ordering from its properties. (Contributed by NM, 29-Jan-1996.) (Revised by Mario Carneiro, 9-Jul-2014.)
Hypotheses
Ref Expression
isso2i.1
isso2i.2
Assertion
Ref Expression
isso2i
Distinct variable groups:   ,,,   ,,,

Proof of Theorem isso2i
StepHypRef Expression
1 equid 1689 . . . . 5
21orci 381 . . . 4
3 eleq1 2498 . . . . . . 7
43anbi2d 686 . . . . . 6
5 equequ2 1699 . . . . . . . 8
6 breq1 4218 . . . . . . . 8
75, 6orbi12d 692 . . . . . . 7
8 breq2 4219 . . . . . . . 8
98notbid 287 . . . . . . 7
107, 9bibi12d 314 . . . . . 6
114, 10imbi12d 313 . . . . 5
12 isso2i.1 . . . . . 6
1312con2bid 321 . . . . 5
1411, 13chvarv 1970 . . . 4
152, 14mpbii 204 . . 3
1615anidms 628 . 2
17 isso2i.2 . 2
1813biimprd 216 . . 3
19 3orass 940 . . . 4
20 df-or 361 . . . 4
2119, 20bitri 242 . . 3
2218, 21sylibr 205 . 2
2316, 17, 22issoi 4537 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wo 359   wa 360   w3o 936   w3a 937   wcel 1726   class class class wbr 4215   wor 4505 This theorem is referenced by:  ltsonq  8851  ltsosr  8974  ltso  9161  xrltso  10739 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-3or 938  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-ral 2712  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-po 4506  df-so 4507
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