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Theorem difss 3126
Description: Subclass relationship for class difference. Exercise 14 of [TakeutiZaring] p. 22. (Contributed by NM, 29-Apr-1994.)
Assertion
Ref Expression
difss  |-  ( A 
\  B )  C_  A

Proof of Theorem difss
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 eldifi 3122 . 2  |-  ( x  e.  ( A  \  B )  ->  x  e.  A )
21ssriv 3029 1  |-  ( A 
\  B )  C_  A
Colors of variables: wff set class
Syntax hints:    \ cdif 2996    C_ wss 2999
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 3001  df-in 3005  df-ss 3012
This theorem is referenced by:  difssd  3127  difss2  3128  ssdifss  3130  0dif  3354  undif1ss  3357  undifabs  3359  inundifss  3360  undifss  3363  unidif  3685  iunxdif2  3778  difexg  3980  reldif  4557  cnvdif  4838  resdif  5275  fndmdif  5404  swoer  6320  swoord1  6321  swoord2  6322  phplem2  6569  phpm  6581  unfiin  6636  sbthlem2  6667  sbthlemi4  6669  sbthlemi5  6670  pinn  6868  niex  6871  dmaddpi  6884  dmmulpi  6885  lerelxr  7549  fisumss  10784  structcnvcnv  11510  strleund  11581  strleun  11582  strle1g  11583
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