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Theorem difss 3043
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 3039 . 2 (x (AB) → x A)
21ssriv 2922 1 (AB) ⊆ A
Colors of variables: wff set class
Syntax hints:  cdif 2887  wss 2890
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 532  ax-in2 533  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-v 2533  df-dif 2893  df-in 2897  df-ss 2904
This theorem is referenced by:  difssd  3044  difss2  3045  ssdifss  3047  0dif  3268  undif1ss  3271  undifabs  3273  inundifss  3274  undifss  3276  difsnpssim  3477  unidif  3582  iunxdif2  3675  difexg  3868  reldif  4380  cnvdif  4653  resdif  5069  fndmdif  5193  swoer  6041  swoord1  6042  swoord2  6043  pinn  6163  niex  6166  dmaddpi  6179  dmmulpi  6180  lerelxr  6684
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