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Theorem dfsmo2 7037
Description: Alternate definition of a strictly monotone ordinal function. (Contributed by Mario Carneiro, 4-Mar-2013.)
Assertion
Ref Expression
dfsmo2
Distinct variable group:   , ,

Proof of Theorem dfsmo2
StepHypRef Expression
1 df-smo 7036 . 2
2 ralcom 3018 . . . . . 6
3 impexp 446 . . . . . . . . 9
4 simpr 461 . . . . . . . . . . 11
5 ordtr1 4926 . . . . . . . . . . . . . . 15
653impib 1194 . . . . . . . . . . . . . 14
763com23 1202 . . . . . . . . . . . . 13
8 simp3 998 . . . . . . . . . . . . 13
97, 8jca 532 . . . . . . . . . . . 12
1093expia 1198 . . . . . . . . . . 11
114, 10impbid2 204 . . . . . . . . . 10
1211imbi1d 317 . . . . . . . . 9
133, 12syl5bbr 259 . . . . . . . 8
1413ralbidv2 2892 . . . . . . 7
1514ralbidva 2893 . . . . . 6
162, 15syl5bb 257 . . . . 5
1716pm5.32i 637 . . . 4
1817anbi2i 694 . . 3
19 3anass 977 . . 3
20 3anass 977 . . 3
2118, 19, 203bitr4i 277 . 2
221, 21bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  e.wcel 1818  A.wral 2807  Ordword 4882   con0 4883  domcdm 5004  -->wf 5589  `cfv 5593  Smowsmo 7035
This theorem is referenced by:  issmo2  7039  smores2  7044  smofvon2  7046
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-ord 4886  df-smo 7036
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