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Theorem 0dif 3538
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 3316 . 2  |-  ( (/)  \  A )  C_  (/)
2 ss0 3498 . 2  |-  ( (
(/)  \  A )  C_  (/)  ->  ( (/)  \  A
)  =  (/) )
31, 2ax-mp 8 1  |-  ( (/)  \  A )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1632    \ cdif 3162    C_ wss 3165   (/)c0 3468
This theorem is referenced by:  fresaun  5428  dffv2  5608  ablfac1eulem  15323  itgioo  19186  ballotlemfval0  23070  ballotlemgun  23099  symdif0  24439  sssu  25244  bwt2  25695
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179  df-nul 3469
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