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Theorem inab 3205
 Description: Intersection of two class abstractions. (Contributed by NM, 29-Sep-2002.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
inab

Proof of Theorem inab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sban 1829 . . 3
2 df-clab 2027 . . 3
3 df-clab 2027 . . . 4
4 df-clab 2027 . . . 4
53, 4anbi12i 433 . . 3
61, 2, 53bitr4ri 202 . 2
76ineqri 3130 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243   wcel 1393  wsb 1645  cab 2026   cin 2916 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924 This theorem is referenced by:  inrab  3209  inrab2  3210  dfrab2  3212  dfrab3  3213  imainlem  4980  imain  4981
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