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Theorem dfoi 7483
 Description: Rewrite df-oi 7482 with abbreviations. (Contributed by Mario Carneiro, 24-Jun-2015.)
Hypotheses
Ref Expression
dfoi.1
dfoi.2
dfoi.3 recs
Assertion
Ref Expression
dfoi OrdIso Se
Distinct variable groups:   ,,,,,,,,   ,,   ,   ,,,,,,,,
Allowed substitution hints:   (,,,,,)   (,,,,,,)   (,,,,,,,)

Proof of Theorem dfoi
StepHypRef Expression
1 df-oi 7482 . 2 OrdIso Se recs recs
2 dfoi.3 . . . . 5 recs
3 dfoi.2 . . . . . . 7
4 dfoi.1 . . . . . . . . . 10
54a1i 11 . . . . . . . . 9
65raleqdv 2912 . . . . . . . . 9
75, 6riotaeqbidv 6555 . . . . . . . 8
87mpteq2ia 4294 . . . . . . 7
93, 8eqtri 2458 . . . . . 6
10 recseq 6637 . . . . . 6 recs recs
119, 10ax-mp 5 . . . . 5 recs recs
122, 11eqtri 2458 . . . 4 recs
1312imaeq1i 5203 . . . . . . . 8 recs
1413raleqi 2910 . . . . . . 7 recs
1514rexbii 2732 . . . . . 6 recs
1615a1i 11 . . . . 5 recs
1716rabbiia 2948 . . . 4 recs
1812, 17reseq12i 5147 . . 3 recs recs
19 ifeq1 3745 . . 3 recs recs Se Se recs recs
2018, 19ax-mp 5 . 2 Se Se recs recs
211, 20eqtr4i 2461 1 OrdIso Se
 Colors of variables: wff set class Syntax hints:   wn 3   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707  wrex 2708  crab 2711  cvv 2958  c0 3630  cif 3741   class class class wbr 4215   cmpt 4269   Se wse 4542   wwe 4543  con0 4584   crn 4882   cres 4883  cima 4884  crio 6545  recscrecs 6635  OrdIsocoi 7481 This theorem is referenced by:  ordtypelem1  7490 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-eu 2287  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-reu 2714  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-uni 4018  df-br 4216  df-opab 4270  df-mpt 4271  df-xp 4887  df-cnv 4889  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fv 5465  df-riota 6552  df-recs 6636  df-oi 7482
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