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Theorem inab 3344
 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 1928 . . 3
2 df-clab 2126 . . 3
3 df-clab 2126 . . . 4
4 df-clab 2126 . . . 4
53, 4anbi12i 455 . . 3
61, 2, 53bitr4ri 212 . 2
76ineqri 3269 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1331   wcel 1480  wsb 1735  cab 2125   cin 3070 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077 This theorem is referenced by:  inrab  3348  inrab2  3349  dfrab2  3351  dfrab3  3352  imainlem  5204  imain  5205  ssenen  6745
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