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Theorem ineq1 3167
 Description: Equality theorem for intersection of two classes. (Contributed by NM, 14-Dec-1993.)
Assertion
Ref Expression
ineq1

Proof of Theorem ineq1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2143 . . . 4
21anbi1d 453 . . 3
3 elin 3156 . . 3
4 elin 3156 . . 3
52, 3, 43bitr4g 221 . 2
65eqrdv 2080 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wceq 1285   wcel 1434   cin 2973 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-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-in 2980 This theorem is referenced by:  ineq2  3168  ineq12  3169  ineq1i  3170  ineq1d  3173  dfrab3ss  3249  intprg  3677  inex1g  3922  reseq1  4634  uzin2  10011  bdinex1g  10877
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