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Theorem 0dif 3861
Description: The difference between the empty set and a class. Part of Exercise 4.4 of [Stoll] p. 16. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
0dif  |-  ( (/)  \  A )  =  (/)

Proof of Theorem 0dif
StepHypRef Expression
1 difss 3594 . 2  |-  ( (/)  \  A )  C_  (/)
2 ss0 3779 . 2  |-  ( (
(/)  \  A )  C_  (/)  ->  ( (/)  \  A
)  =  (/) )
31, 2ax-mp 5 1  |-  ( (/)  \  A )  =  (/)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370    \ cdif 3436    C_ wss 3439   (/)c0 3748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3080  df-dif 3442  df-in 3446  df-ss 3453  df-nul 3749
This theorem is referenced by:  fresaun  5693  dffv2  5876  ablfac1eulem  16705  bwthOLD  19156  itgioo  21436  imadifxp  26117  sibf0  26887  ballotlemfval0  27045  ballotlemgun  27074  symdif0  28022
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