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Theorem difss 3070
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 3066 . 2 (𝑥 ∈ (𝐴𝐵) → 𝑥𝐴)
21ssriv 2949 1 (𝐴𝐵) ⊆ 𝐴
Colors of variables: wff set class
Syntax hints:  cdif 2914  wss 2917
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-dif 2920  df-in 2924  df-ss 2931
This theorem is referenced by:  difssd  3071  difss2  3072  ssdifss  3074  0dif  3295  undif1ss  3298  undifabs  3300  inundifss  3301  undifss  3303  difsnpssim  3507  unidif  3612  iunxdif2  3705  difexg  3898  reldif  4457  cnvdif  4730  resdif  5148  fndmdif  5272  swoer  6134  swoord1  6135  swoord2  6136  phplem2  6316  phpm  6327  pinn  6405  niex  6408  dmaddpi  6421  dmmulpi  6422  lerelxr  7080
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