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Theorem ssrin 3328
 Description: Add right intersection to subclass relation. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
ssrin

Proof of Theorem ssrin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssel 3118 . . . 4
21anim1d 334 . . 3
3 elin 3286 . . 3
4 elin 3286 . . 3
52, 3, 43imtr4g 204 . 2
65ssrdv 3130 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wcel 2125   cin 3097   wss 3098 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-in 3104  df-ss 3111 This theorem is referenced by:  sslin  3329  ssrind  3330  ss2in  3331  ssdisj  3446  ssdifin0  3471  ssres  4885  phplem2  6787  sbthlem7  6896  fiss  6910  tgss  12410  metrest  12853
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