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Theorem elintab 4063
 Description: Membership in the intersection of a class abstraction. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
inteqab.1
Assertion
Ref Expression
elintab
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem elintab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 inteqab.1 . . 3
21elint 4058 . 2
3 nfsab1 2428 . . . 4
4 nfv 1630 . . . 4
53, 4nfim 1833 . . 3
6 nfv 1630 . . 3
7 eleq1 2498 . . . . 5
8 abid 2426 . . . . 5
97, 8syl6bb 254 . . . 4
10 eleq2 2499 . . . 4
119, 10imbi12d 313 . . 3
125, 6, 11cbval 1983 . 2
132, 12bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550   wcel 1726  cab 2424  cvv 2958  cint 4052 This theorem is referenced by:  elintrab  4064  intmin4  4081  intab  4082  intid  4424  dfom3  7605  dfom5  7608  tc2  7684  dfnn2  10018  efgi  15356  efgi2  15362  heibor1lem  26532 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-v 2960  df-int 4053
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