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Theorem 0dif 3526
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 3304 . 2  |-  ( (/)  \  A )  C_  (/)
2 ss0 3486 . 2  |-  ( (
(/)  \  A )  C_  (/)  ->  ( (/)  \  A
)  =  (/) )
31, 2ax-mp 10 1  |-  ( (/)  \  A )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1624    \ cdif 3150    C_ wss 3153   (/)c0 3456
This theorem is referenced by:  fresaun  5377  dffv2  5553  ablfac1eulem  15301  itgioo  19164  ballotlemfval0  23047  ballotlemgun  23076  symdif0  23776  sssu  24540  bwt2  24991
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1867  ax-ext 2265
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-v 2791  df-dif 3156  df-in 3160  df-ss 3167  df-nul 3457
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