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Theorem dif0 3620
 Description: The difference between a class and the empty set. Part of Exercise 4.4 of [Stoll] p. 16. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
dif0 (A ) = A

Proof of Theorem dif0
StepHypRef Expression
1 difid 3618 . . 3 (A A) =
21difeq2i 3382 . 2 (A (A A)) = (A )
3 difdif 3392 . 2 (A (A A)) = A
42, 3eqtr3i 2375 1 (A ) = A
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∖ cdif 3206  ∅c0 3550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551 This theorem is referenced by:  undifv  3624
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