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Theorem nfoi 8038
 Description: Hypothesis builder for ordinal isomorphism. (Contributed by Mario Carneiro, 23-May-2015.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
nfoi.1
nfoi.2
Assertion
Ref Expression
nfoi OrdIso

Proof of Theorem nfoi
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-oi 8034 . 2 OrdIso Se recs recs
2 nfoi.1 . . . . 5
3 nfoi.2 . . . . 5
42, 3nfwe 4829 . . . 4
52, 3nfse 4828 . . . 4 Se
64, 5nfan 1988 . . 3 Se
7 nfcv 2580 . . . . . 6
8 nfcv 2580 . . . . . . . . . 10
9 nfcv 2580 . . . . . . . . . . 11
10 nfcv 2580 . . . . . . . . . . 11
119, 2, 10nfbr 4468 . . . . . . . . . 10
128, 11nfral 2808 . . . . . . . . 9
1312, 3nfrab 3007 . . . . . . . 8
14 nfcv 2580 . . . . . . . . . 10
15 nfcv 2580 . . . . . . . . . 10
1614, 2, 15nfbr 4468 . . . . . . . . 9
1716nfn 1960 . . . . . . . 8
1813, 17nfral 2808 . . . . . . 7
1918, 13nfriota 6276 . . . . . 6
207, 19nfmpt 4512 . . . . 5
2120nfrecs 7104 . . . 4 recs
22 nfcv 2580 . . . . . . . 8
2321, 22nfima 5195 . . . . . . 7 recs
24 nfcv 2580 . . . . . . . 8
25 nfcv 2580 . . . . . . . 8
2624, 2, 25nfbr 4468 . . . . . . 7
2723, 26nfral 2808 . . . . . 6 recs
283, 27nfrex 2885 . . . . 5 recs
29 nfcv 2580 . . . . 5
3028, 29nfrab 3007 . . . 4 recs
3121, 30nfres 5126 . . 3 recs recs
32 nfcv 2580 . . 3
336, 31, 32nfif 3940 . 2 Se recs recs
341, 33nfcxfr 2578 1 OrdIso
 Colors of variables: wff setvar class Syntax hints:   wn 3   wa 370  wnfc 2566  wral 2771  wrex 2772  crab 2775  cvv 3080  c0 3761  cif 3911   class class class wbr 4423   cmpt 4482   Se wse 4810   wwe 4811   crn 4854   cres 4855  cima 4856  con0 5442  crio 6266  recscrecs 7100  OrdIsocoi 8033 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-rex 2777  df-rab 2780  df-v 3082  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3912  df-sn 3999  df-pr 4001  df-op 4005  df-uni 4220  df-br 4424  df-opab 4483  df-mpt 4484  df-po 4774  df-so 4775  df-fr 4812  df-se 4813  df-we 4814  df-xp 4859  df-cnv 4861  df-dm 4863  df-rn 4864  df-res 4865  df-ima 4866  df-pred 5399  df-iota 5565  df-fv 5609  df-riota 6267  df-wrecs 7039  df-recs 7101  df-oi 8034 This theorem is referenced by:  hsmexlem2  8864
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