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Theorem fliftfuns 6028
 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
Assertion
Ref Expression
fliftfuns
Distinct variable groups:   ,,   ,,   ,,,   ,,   ,,,   ,,,   ,,,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem fliftfuns
StepHypRef Expression
1 flift.1 . . 3
2 nfcv 2571 . . . . 5
3 nfcsb1v 3275 . . . . . 6
4 nfcsb1v 3275 . . . . . 6
53, 4nfop 3992 . . . . 5
6 csbeq1a 3251 . . . . . 6
7 csbeq1a 3251 . . . . . 6
86, 7opeq12d 3984 . . . . 5
92, 5, 8cbvmpt 4291 . . . 4
109rneqi 5088 . . 3
111, 10eqtri 2455 . 2
12 flift.2 . . . 4
1312ralrimiva 2781 . . 3
143nfel1 2581 . . . 4
156eleq1d 2501 . . . 4
1614, 15rspc 3038 . . 3
1713, 16mpan9 456 . 2
18 flift.3 . . . 4
1918ralrimiva 2781 . . 3
204nfel1 2581 . . . 4
217eleq1d 2501 . . . 4
2220, 21rspc 3038 . . 3
2319, 22mpan9 456 . 2
24 csbeq1 3246 . 2
25 csbeq1 3246 . 2
2611, 17, 23, 24, 25fliftfun 6026 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wral 2697  csb 3243  cop 3809   cmpt 4258   crn 4871   wfun 5440 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-fv 5454
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