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Theorem smoel2 7053
 Description: A strictly monotone ordinal function preserves the epsilon relation. (Contributed by Mario Carneiro, 12-Mar-2013.)
Assertion
Ref Expression
smoel2

Proof of Theorem smoel2
StepHypRef Expression
1 fndm 5685 . . . . . 6
21eleq2d 2527 . . . . 5
32anbi1d 704 . . . 4
43biimprd 223 . . 3
5 smoel 7050 . . . 4
653expib 1199 . . 3
74, 6sylan9 657 . 2
87imp 429 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  e.wcel 1818  domcdm 5004  Fnwfn 5588  cfv 5593  Smo`wsmo 7035 This theorem is referenced by:  smo11  7054  smoord  7055  smogt  7057  cofsmo  8670 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-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-tr 4546  df-ord 4886  df-iota 5556  df-fn 5596  df-fv 5601  df-smo 7036
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