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Theorem issmo2 6614
 Description: Alternative definition of a strictly monotone ordinal function. (Contributed by Mario Carneiro, 12-Mar-2013.)
Assertion
Ref Expression
issmo2
Distinct variable groups:   ,   ,,
Allowed substitution hints:   ()   (,)

Proof of Theorem issmo2
StepHypRef Expression
1 fss 5602 . . . . 5
21ex 425 . . . 4
3 fdm 5598 . . . . 5
43feq2d 5584 . . . 4
52, 4sylibrd 227 . . 3
6 ordeq 4591 . . . . 5
73, 6syl 16 . . . 4
87biimprd 216 . . 3
93raleqdv 2912 . . . 4
109biimprd 216 . . 3
115, 8, 103anim123d 1262 . 2
12 dfsmo2 6612 . 2
1311, 12syl6ibr 220 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   w3a 937   wceq 1653   wcel 1726  wral 2707   wss 3322   word 4583  con0 4584   cdm 4881  wf 5453  cfv 5457   wsmo 6610 This theorem is referenced by:  alephsmo  7988  cofsmo  8154  cfsmolem  8155 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-ral 2712  df-rex 2713  df-v 2960  df-in 3329  df-ss 3336  df-uni 4018  df-tr 4306  df-po 4506  df-so 4507  df-fr 4544  df-we 4546  df-ord 4587  df-fn 5460  df-f 5461  df-smo 6611
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