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Theorem elintrab 4298
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:   ,

Proof of Theorem elintrab
StepHypRef Expression
1 inteqab.1 . . . 4
21elintab 4297 . . 3
3 impexp 446 . . . 4
43albii 1640 . . 3
52, 4bitri 249 . 2
6 df-rab 2816 . . . 4
76inteqi 4290 . . 3
87eleq2i 2535 . 2
9 df-ral 2812 . 2
105, 8, 93bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  e.wcel 1818  {cab 2442  A.wral 2807  {crab 2811   cvv 3109  |^|cint 4286
This theorem is referenced by:  elintrabg  4299  intmin  4306  rankunb  8289  isf34lem4  8778  ist1-3  19850  filufint  20421  elspani  26461  kur14lem9  28658  lcosslsp  33039  pclclN  35615  elpclN  35616
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-int 4287
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