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Theorem 0dif 3635
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 3410 . 2  |-  ( (/)  \  A )  C_  (/)
2 ss0 3594 . 2  |-  ( (
(/)  \  A )  C_  (/)  ->  ( (/)  \  A
)  =  (/) )
31, 2ax-mp 8 1  |-  ( (/)  \  A )  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1649    \ cdif 3253    C_ wss 3256   (/)c0 3564
This theorem is referenced by:  fresaun  5547  dffv2  5728  ablfac1eulem  15550  itgioo  19567  imadifxp  23874  ballotlemfval0  24525  ballotlemgun  24554  symdif0  25385
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-v 2894  df-dif 3259  df-in 3263  df-ss 3270  df-nul 3565
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