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Theorem cnfcom3c 8150
 Description: Wrap the construction of cnfcom3 8148 into an existence quantifier. For any , there is a bijection from to some power of . Furthermore, this bijection is canonical , which means that we can find a single function which will give such bijections for every less than some arbitrarily large bound . (Contributed by Mario Carneiro, 30-May-2015.)
Assertion
Ref Expression
cnfcom3c
Distinct variable group:   ,,,

Proof of Theorem cnfcom3c
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2467 . 2 CNF CNF
2 eqid 2467 . 2 CNF CNF
3 eqid 2467 . 2 OrdIso CNF supp OrdIso CNF supp
4 eqid 2467 . 2 seq𝜔 OrdIso CNF supp CNF OrdIso CNF supp seq𝜔 OrdIso CNF supp CNF OrdIso CNF supp
5 eqid 2467 . 2 seq𝜔 OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp seq𝜔 OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp
6 eqid 2467 . 2 OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp
7 eqid 2467 . 2 OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp
8 eqid 2467 . 2 OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp
9 eqid 2467 . 2 CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp
10 eqid 2467 . 2 CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp
11 eqid 2467 . 2 CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp seq𝜔 OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp seq𝜔 OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp
12 eqid 2467 . 2 CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp seq𝜔 OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp OrdIso CNF supp seq𝜔 OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp CNF OrdIso CNF supp OrdIso CNF supp
131, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12cnfcom3clem 8149 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wex 1596   wcel 1767  wral 2814  wrex 2815  cvv 3113   cdif 3473   cun 3474   wss 3476  c0 3785  cuni 4245   cmpt 4505   cep 4789  con0 4878  ccnv 4998   cdm 4999   ccom 5003  wf1o 5587  cfv 5588  (class class class)co 6284   cmpt2 6286  com 6684   supp csupp 6901  seq𝜔cseqom 7112  c1o 7123   coa 7127   comu 7128   coe 7129  OrdIsocoi 7934   CNF ccnf 8078 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-rep 4558  ax-sep 4568  ax-nul 4576  ax-pow 4625  ax-pr 4686  ax-un 6576  ax-inf2 8058 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1382  df-fal 1385  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-reu 2821  df-rmo 2822  df-rab 2823  df-v 3115  df-sbc 3332  df-csb 3436  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-pss 3492  df-nul 3786  df-if 3940  df-pw 4012  df-sn 4028  df-pr 4030  df-tp 4032  df-op 4034  df-uni 4246  df-int 4283  df-iun 4327  df-br 4448  df-opab 4506  df-mpt 4507  df-tr 4541  df-eprel 4791  df-id 4795  df-po 4800  df-so 4801  df-fr 4838  df-se 4839  df-we 4840  df-ord 4881  df-on 4882  df-lim 4883  df-suc 4884  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-rn 5010  df-res 5011  df-ima 5012  df-iota 5551  df-fun 5590  df-fn 5591  df-f 5592  df-f1 5593  df-fo 5594  df-f1o 5595  df-fv 5596  df-isom 5597  df-riota 6245  df-ov 6287  df-oprab 6288  df-mpt2 6289  df-om 6685  df-1st 6784  df-2nd 6785  df-supp 6902  df-recs 7042  df-rdg 7076  df-seqom 7113  df-1o 7130  df-2o 7131  df-oadd 7134  df-omul 7135  df-oexp 7136  df-er 7311  df-map 7422  df-en 7517  df-dom 7518  df-sdom 7519  df-fin 7520  df-fsupp 7830  df-oi 7935  df-cnf 8079 This theorem is referenced by:  infxpenc2  8399
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