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Theorem difss 3064
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 3060 . 2 (x (AB) → x A)
21ssriv 2943 1 (AB) ⊆ A
Colors of variables: wff set class
Syntax hints:  cdif 2908  wss 2911
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914  df-in 2918  df-ss 2925
This theorem is referenced by:  difssd  3065  difss2  3066  ssdifss  3068  0dif  3289  undif1ss  3292  undifabs  3294  inundifss  3295  undifss  3297  difsnpssim  3498  unidif  3603  iunxdif2  3696  difexg  3889  reldif  4400  cnvdif  4673  resdif  5091  fndmdif  5215  swoer  6070  swoord1  6071  swoord2  6072  pinn  6293  niex  6296  dmaddpi  6309  dmmulpi  6310  lerelxr  6859
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