Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  qliftfund Unicode version

Theorem qliftfund 7039
 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 425 . . 3
32alrimivv 1644 . 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 7038 . 2
103, 9mpbird 225 1
 Colors of variables: wff set class Syntax hints:  ->wi 4  /\wa 360  A.wal 1550  =wceq 1654  e.wcel 1728   cvv 2965  <.cop 3844   class class class wbr 4243  e.cmpt 4301  rancrn 4920  Funwfun 5495  Erwer 6951  [`cec 6952 This theorem is referenced by:  orbstafun  15139  frgpupf  15456 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-13 1730  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4364  ax-nul 4372  ax-pow 4416  ax-pr 4442  ax-un 4742 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-mo 2293  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2717  df-rex 2718  df-rab 2721  df-v 2967  df-sbc 3171  df-csb 3271  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3766  df-pw 3828  df-sn 3847  df-pr 3848  df-op 3850  df-uni 4044  df-br 4244  df-opab 4302  df-mpt 4303  df-id 4539  df-xp 4925  df-rel 4926  df-cnv 4927  df-co 4928  df-dm 4929  df-rn 4930  df-res 4931  df-ima 4932  df-iota 5464  df-fun 5503  df-fn 5504  df-f 5505  df-fv 5509  df-er 6954  df-ec 6956  df-qs 6960
 Copyright terms: Public domain W3C validator