Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  qliftfund Unicode version

Theorem qliftfund 6189
 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
qlift.1
qlift.2
qlift.3
qlift.4
qliftfun.4
qliftfund.6
Assertion
Ref Expression
qliftfund
Distinct variable groups:   ,   ,   ,,   ,,   ,   ,,   ,,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem qliftfund
StepHypRef Expression
1 qliftfund.6 . . . 4
21ex 108 . . 3
32alrimivv 1755 . 2
4 qlift.1 . . 3
5 qlift.2 . . 3
6 qlift.3 . . 3
7 qlift.4 . . 3
8 qliftfun.4 . . 3
94, 5, 6, 7, 8qliftfun 6188 . 2
103, 9mpbird 156 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wal 1241   wceq 1243   wcel 1393  cvv 2557  cop 3378   class class class wbr 3764   cmpt 3818   crn 4346   wfun 4896   wer 6103  cec 6104 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944  ax-un 4170 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-rab 2315  df-v 2559  df-sbc 2765  df-csb 2853  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-opab 3819  df-mpt 3820  df-id 4030  df-xp 4351  df-rel 4352  df-cnv 4353  df-co 4354  df-dm 4355  df-rn 4356  df-res 4357  df-ima 4358  df-iota 4867  df-fun 4904  df-fn 4905  df-f 4906  df-fv 4910  df-er 6106  df-ec 6108  df-qs 6112 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator