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Theorem isso2i 4786
 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 1854 . . . . 5
21orci 392 . . . 4
3 eleq1 2516 . . . . . . 7
43anbi2d 709 . . . . . 6
5 equequ2 1867 . . . . . . . 8
6 breq1 4404 . . . . . . . 8
75, 6orbi12d 715 . . . . . . 7
8 breq2 4405 . . . . . . . 8
98notbid 296 . . . . . . 7
107, 9bibi12d 323 . . . . . 6
114, 10imbi12d 322 . . . . 5
12 isso2i.1 . . . . . 6
1312con2bid 331 . . . . 5
1411, 13chvarv 2106 . . . 4
152, 14mpbii 215 . . 3
1615anidms 650 . 2
17 isso2i.2 . 2
1813biimprd 227 . . 3
19 3orass 987 . . . 4
20 df-or 372 . . . 4
2119, 20bitri 253 . . 3
2218, 21sylibr 216 . 2
2316, 17, 22issoi 4785 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wo 370   wa 371   w3o 983   w3a 984   wcel 1886   class class class wbr 4401   wor 4753 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 985  df-3an 986  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ral 2741  df-rab 2745  df-v 3046  df-dif 3406  df-un 3408  df-in 3410  df-ss 3417  df-nul 3731  df-if 3881  df-sn 3968  df-pr 3970  df-op 3974  df-br 4402  df-po 4754  df-so 4755 This theorem is referenced by:  ltsonq  9391  ltsosr  9515  ltso  9711  xrltso  11437
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