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Theorem fliftel 6033
 Description: Elementhood in the relation . (Contributed by Mario Carneiro, 23-Dec-2016.)
Hypotheses
Ref Expression
flift.1
flift.2
flift.3
Assertion
Ref Expression
fliftel
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem fliftel
StepHypRef Expression
1 df-br 4215 . . 3
2 flift.1 . . . 4
32eleq2i 2502 . . 3
4 eqid 2438 . . . 4
5 opex 4429 . . . 4
64, 5elrnmpti 5123 . . 3
71, 3, 63bitri 264 . 2
8 flift.2 . . . 4
9 flift.3 . . . 4
10 opthg2 4439 . . . 4
118, 9, 10syl2anc 644 . . 3
1211rexbidva 2724 . 2
137, 12syl5bb 250 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wrex 2708  cop 3819   class class class wbr 4214   cmpt 4268   crn 4881 This theorem is referenced by:  fliftcnv  6035  fliftfun  6036  fliftf  6039  fliftval  6040  qliftel  6989 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 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 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-mpt 4270  df-cnv 4888  df-dm 4890  df-rn 4891
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