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Theorem difss 3276
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 3272 . 2 (𝑥 ∈ (𝐴𝐵) → 𝑥𝐴)
21ssriv 3174 1 (𝐴𝐵) ⊆ 𝐴
Colors of variables: wff set class
Syntax hints:  cdif 3141  wss 3144
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-dif 3146  df-in 3150  df-ss 3157
This theorem is referenced by:  difssd  3277  difss2  3278  ssdifss  3280  0dif  3509  undif1ss  3512  undifabs  3514  inundifss  3515  undifss  3518  unidif  3856  iunxdif2  3950  difexg  4159  exmid1stab  4226  reldif  4764  cnvdif  5053  resdif  5502  fndmdif  5641  swoer  6586  swoord1  6587  swoord2  6588  phplem2  6880  phpm  6892  unfiin  6953  sbthlem2  6986  sbthlemi4  6988  sbthlemi5  6989  difinfinf  7129  pinn  7337  niex  7340  dmaddpi  7353  dmmulpi  7354  lerelxr  8049  fisumss  11431  fprodssdc  11629  structcnvcnv  12527  strleund  12612  strleun  12613  strle1g  12615  discld  14088
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