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Theorem difss 3202
Description: Subclass relationship for class difference. Exercise 14 of [TakeutiZaring] p. 22. (Contributed by NM, 29-Apr-1994.)
Assertion
Ref Expression
difss (𝐴𝐵) ⊆ 𝐴

Proof of Theorem difss
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 eldifi 3198 . 2 (𝑥 ∈ (𝐴𝐵) → 𝑥𝐴)
21ssriv 3101 1 (𝐴𝐵) ⊆ 𝐴
Colors of variables: wff set class
Syntax hints:  cdif 3068  wss 3071
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-dif 3073  df-in 3077  df-ss 3084
This theorem is referenced by:  difssd  3203  difss2  3204  ssdifss  3206  0dif  3434  undif1ss  3437  undifabs  3439  inundifss  3440  undifss  3443  unidif  3768  iunxdif2  3861  difexg  4069  reldif  4659  cnvdif  4945  resdif  5389  fndmdif  5525  swoer  6457  swoord1  6458  swoord2  6459  phplem2  6747  phpm  6759  unfiin  6814  sbthlem2  6846  sbthlemi4  6848  sbthlemi5  6849  difinfinf  6986  pinn  7124  niex  7127  dmaddpi  7140  dmmulpi  7141  lerelxr  7834  fisumss  11168  structcnvcnv  11985  strleund  12057  strleun  12058  strle1g  12059  discld  12315  exmid1stab  13209
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