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Theorem difss 3098
 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 3094 . 2 (𝑥 ∈ (𝐴𝐵) → 𝑥𝐴)
21ssriv 2977 1 (𝐴𝐵) ⊆ 𝐴
 Colors of variables: wff set class Syntax hints:   ∖ cdif 2942   ⊆ wss 2945 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-dif 2948  df-in 2952  df-ss 2959 This theorem is referenced by:  difssd  3099  difss2  3100  ssdifss  3102  0dif  3323  undif1ss  3326  undifabs  3328  inundifss  3329  undifss  3331  difsnpssim  3535  unidif  3640  iunxdif2  3733  difexg  3926  reldif  4485  cnvdif  4758  resdif  5176  fndmdif  5300  swoer  6165  swoord1  6166  swoord2  6167  phplem2  6347  phpm  6358  pinn  6465  niex  6468  dmaddpi  6481  dmmulpi  6482  lerelxr  7141
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