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Theorem difab 3240
 Description: Difference of two class abstractions. (Contributed by NM, 23-Oct-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
difab

Proof of Theorem difab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-clab 2069 . . 3
2 sban 1871 . . 3
3 df-clab 2069 . . . . 5
43bicomi 130 . . . 4
5 sbn 1868 . . . . 5
6 df-clab 2069 . . . . 5
75, 6xchbinxr 641 . . . 4
84, 7anbi12i 448 . . 3
91, 2, 83bitrri 205 . 2
109difeqri 3093 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 102   wceq 1285   wcel 1434  wsb 1686  cab 2068   cdif 2971 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-in1 577  ax-in2 578  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-fal 1291  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-dif 2976 This theorem is referenced by:  notab  3241  difrab  3245  notrab  3248  imadiflem  5009  imadif  5010
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