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Theorem fliftel 6207
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:   ,   ,   ,   ,   ,   ,S

Proof of Theorem fliftel
StepHypRef Expression
1 df-br 4453 . . 3
2 flift.1 . . . 4
32eleq2i 2535 . . 3
4 eqid 2457 . . . 4
5 opex 4716 . . . 4
64, 5elrnmpti 5258 . . 3
71, 3, 63bitri 271 . 2
8 flift.2 . . . 4
9 flift.3 . . . 4
10 opthg2 4729 . . . 4
118, 9, 10syl2anc 661 . . 3
1211rexbidva 2965 . 2
137, 12syl5bb 257 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E.wrex 2808  <.cop 4035   class class class wbr 4452  e.cmpt 4510  rancrn 5005
This theorem is referenced by:  fliftcnv  6209  fliftfun  6210  fliftf  6213  fliftval  6214  qliftel  7413
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-mpt 4512  df-cnv 5012  df-dm 5014  df-rn 5015
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