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Theorem difab 3748
 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 2415 . . 3
2 sban 2194 . . 3
3 df-clab 2415 . . . . 5
43bicomi 205 . . . 4
5 sbn 2186 . . . . 5
6 df-clab 2415 . . . . 5
75, 6xchbinxr 312 . . . 4
84, 7anbi12i 701 . . 3
91, 2, 83bitrri 275 . 2
109difeqri 3591 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wa 370   wceq 1437  wsb 1789   wcel 1870  cab 2414   cdif 3439 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-v 3089  df-dif 3445 This theorem is referenced by:  notab  3749  difrab  3753  notrab  3756
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