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Theorem difab 3766
 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 2443 . . 3
2 sban 2140 . . 3
3 df-clab 2443 . . . . 5
43bicomi 202 . . . 4
5 sbn 2132 . . . . 5
6 df-clab 2443 . . . . 5
75, 6xchbinxr 311 . . . 4
84, 7anbi12i 697 . . 3
91, 2, 83bitrri 272 . 2
109difeqri 3623 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  /\wa 369  =wceq 1395  [wsb 1739  e.wcel 1818  {cab 2442  \cdif 3472 This theorem is referenced by:  notab  3767  difrab  3771  notrab  3774 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-dif 3478
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