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Theorem fliftfund 6221
 Description: The function is the unique function defined by , provided that the well-definedness condition holds. (Contributed by Mario Carneiro, 23-Dec-2016.)
Hypotheses
Ref Expression
flift.1
flift.2
flift.3
fliftfun.4
fliftfun.5
fliftfund.6
Assertion
Ref Expression
fliftfund
Distinct variable groups:   ,   ,   ,   ,,   ,   ,   ,,   ,,   ,,
Allowed substitution hints:   ()   ()   ()   ()   ()

Proof of Theorem fliftfund
StepHypRef Expression
1 fliftfund.6 . . . . 5
213exp2 1223 . . . 4
32imp32 434 . . 3
43ralrimivva 2853 . 2
5 flift.1 . . 3
6 flift.2 . . 3
7 flift.3 . . 3
8 fliftfun.4 . . 3
9 fliftfun.5 . . 3
105, 6, 7, 8, 9fliftfun 6220 . 2
114, 10mpbird 235 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   w3a 982   wceq 1437   wcel 1870  wral 2782  cop 4008   cmpt 4484   crn 4855   wfun 5595 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-csb 3402  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-res 4866  df-ima 4867  df-iota 5565  df-fun 5603  df-fn 5604  df-f 5605  df-fv 5609 This theorem is referenced by:  cygznlem2a  19069  pi1xfrf  21977  pi1cof  21983
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