New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  dfdif2 GIF version

Theorem dfdif2 3222
 Description: Alternate definition of class difference. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
dfdif2 (A B) = {x A ¬ x B}
Distinct variable groups:   x,A   x,B

Proof of Theorem dfdif2
StepHypRef Expression
1 eldif 3221 . . 3 (x (A B) ↔ (x A ¬ x B))
21abbi2i 2464 . 2 (A B) = {x (x A ¬ x B)}
3 df-rab 2623 . 2 {x A ¬ x B} = {x (x A ¬ x B)}
42, 3eqtr4i 2376 1 (A B) = {x A ¬ x B}
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∧ wa 358   = wceq 1642   ∈ wcel 1710  {cab 2339  {crab 2618   ∖ 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-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215 This theorem is referenced by:  difidALT  3619
 Copyright terms: Public domain W3C validator