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Theorem elintrab 4064
 Description: Membership in the intersection of a class abstraction. (Contributed by NM, 17-Oct-1999.)
Hypothesis
Ref Expression
inteqab.1
Assertion
Ref Expression
elintrab
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elintrab
StepHypRef Expression
1 inteqab.1 . . . 4
21elintab 4063 . . 3
3 impexp 435 . . . 4
43albii 1576 . . 3
52, 4bitri 242 . 2
6 df-rab 2716 . . . 4
76inteqi 4056 . . 3
87eleq2i 2502 . 2
9 df-ral 2712 . 2
105, 8, 93bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wcel 1726  cab 2424  wral 2707  crab 2711  cvv 2958  cint 4052 This theorem is referenced by:  elintrabg  4065  intmin  4072  rankunb  7778  isf34lem4  8259  ist1-3  17415  filufint  17954  elspani  23047  kur14lem9  24902  pclclN  30690  elpclN  30691 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-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rab 2716  df-v 2960  df-int 4053
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