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Theorem difab 3523
 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 2340 . . 3
2 sban 2069 . . 3
3 df-clab 2340 . . . . 5
43bicomi 193 . . . 4
5 sbn 2062 . . . . 5
6 df-clab 2340 . . . . 5
75, 6xchbinxr 302 . . . 4
84, 7anbi12i 678 . . 3
91, 2, 83bitrri 263 . 2
109difeqri 3387 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wa 358   wceq 1642  wsb 1648   wcel 1710  cab 2339   cdif 3206 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215 This theorem is referenced by:  notab  3525  difrab  3529  notrab  3532
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