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Theorem inab 3611
 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 2141 . . 3
2 df-clab 2425 . . 3
3 df-clab 2425 . . . 4
4 df-clab 2425 . . . 4
53, 4anbi12i 680 . . 3
61, 2, 53bitr4ri 271 . 2
76ineqri 3536 1
 Colors of variables: wff set class Syntax hints:   wa 360   wceq 1653  wsb 1659   wcel 1726  cab 2424   cin 3321 This theorem is referenced by:  inrab  3615  inrab2  3616  dfrab2  3618  dfrab3  3619  orduniss2  4815  ssenen  7283  hashf1lem2  11707  ballotlem2  24748  dfiota3  25770  diophin  26833 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-v 2960  df-in 3329
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