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Theorem bj-elccinfty 31401
 Description: A lemma for infinite extended complex numbers. (Contributed by BJ, 27-Jun-2019.)
Assertion
Ref Expression
bj-elccinfty inftyexpi CCinfty

Proof of Theorem bj-elccinfty
StepHypRef Expression
1 df-bj-inftyexpi 31394 . . . . 5 inftyexpi
21funmpt2 5638 . . . 4 inftyexpi
32jctl 543 . . 3 inftyexpi inftyexpi inftyexpi
4 opex 4686 . . . . 5
54, 1dmmpti 5725 . . . 4 inftyexpi
65eqcomi 2442 . . 3 inftyexpi
73, 6eleq2s 2537 . 2 inftyexpi inftyexpi
8 fvelrn 6030 . 2 inftyexpi inftyexpi inftyexpi inftyexpi
9 df-bj-ccinfty 31399 . . . . 5 CCinfty inftyexpi
109eqcomi 2442 . . . 4 inftyexpi CCinfty
1110eleq2i 2507 . . 3 inftyexpi inftyexpi inftyexpi CCinfty
1211biimpi 197 . 2 inftyexpi inftyexpi inftyexpi CCinfty
137, 8, 123syl 18 1 inftyexpi CCinfty
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wcel 1870  cop 4008   cdm 4854   crn 4855   wfun 5595  cfv 5601  (class class class)co 6305  cc 9536  cneg 9860  cioc 11636  cpi 14097  inftyexpi cinftyexpi 31393  CCinftycccinfty 31398 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pr 4661 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-sbc 3306  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-uni 4223  df-br 4427  df-opab 4485  df-mpt 4486  df-id 4769  df-xp 4860  df-rel 4861  df-cnv 4862  df-co 4863  df-dm 4864  df-rn 4865  df-iota 5565  df-fun 5603  df-fn 5604  df-fv 5609  df-bj-inftyexpi 31394  df-bj-ccinfty 31399 This theorem is referenced by:  bj-pinftyccb  31408
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