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Theorem qliftfun 6981
 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
Assertion
Ref Expression
qliftfun
Distinct variable groups:   ,   ,   ,,   ,,   ,   ,,   ,,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem qliftfun
StepHypRef Expression
1 qlift.1 . . 3
2 qlift.2 . . . 4
3 qlift.3 . . . 4
4 qlift.4 . . . 4
51, 2, 3, 4qliftlem 6977 . . 3
6 eceq1 6933 . . 3
7 qliftfun.4 . . 3
81, 5, 2, 6, 7fliftfun 6026 . 2
93adantr 452 . . . . . . . . . . 11
10 simpr 448 . . . . . . . . . . 11
119, 10ercl 6908 . . . . . . . . . 10
129, 10ercl2 6910 . . . . . . . . . 10
1311, 12jca 519 . . . . . . . . 9
1413ex 424 . . . . . . . 8
1514pm4.71rd 617 . . . . . . 7
163adantr 452 . . . . . . . . 9
17 simprl 733 . . . . . . . . 9
1816, 17erth 6941 . . . . . . . 8
1918pm5.32da 623 . . . . . . 7
2015, 19bitrd 245 . . . . . 6
2120imbi1d 309 . . . . 5
22 impexp 434 . . . . 5
2321, 22syl6bb 253 . . . 4
24232albidv 1637 . . 3
25 r2al 2734 . . 3
2624, 25syl6bbr 255 . 2
278, 26bitr4d 248 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wceq 1652   wcel 1725  wral 2697  cvv 2948  cop 3809   class class class wbr 4204   cmpt 4258   crn 4871   wfun 5440   wer 6894  cec 6895  cqs 6896 This theorem is referenced by:  qliftfund  6982  qliftfuns  6983 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-13 1727  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-pow 4369  ax-pr 4395  ax-un 4693 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-pw 3793  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  df-er 6897  df-ec 6899  df-qs 6903
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