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Theorem fliftel1 5465
 Description: Elementhood in the relation . (Contributed by Mario Carneiro, 23-Dec-2016.)
Hypotheses
Ref Expression
flift.1
flift.2
flift.3
Assertion
Ref Expression
fliftel1
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem fliftel1
StepHypRef Expression
1 flift.2 . . . . 5
2 flift.3 . . . . 5
3 opexg 3991 . . . . 5
41, 2, 3syl2anc 403 . . . 4
5 eqid 2082 . . . . . 6
65elrnmpt1 4613 . . . . 5
76adantll 460 . . . 4
84, 7mpdan 412 . . 3
9 flift.1 . . 3
108, 9syl6eleqr 2173 . 2
11 df-br 3794 . 2
1210, 11sylibr 132 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wceq 1285   wcel 1434  cvv 2602  cop 3409   class class class wbr 3793   cmpt 3847   crn 4372 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-sbc 2817  df-csb 2910  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-mpt 3849  df-cnv 4379  df-dm 4381  df-rn 4382 This theorem is referenced by:  fliftfun  5467  qliftel1  6253
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