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Theorem sscon 3241
 Description: Contraposition law for subsets. Exercise 15 of [TakeutiZaring] p. 22. (Contributed by NM, 22-Mar-1998.)
Assertion
Ref Expression
sscon

Proof of Theorem sscon
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssel 3122 . . . . 5
21con3d 621 . . . 4
32anim2d 335 . . 3
4 eldif 3111 . . 3
5 eldif 3111 . . 3
63, 4, 53imtr4g 204 . 2
76ssrdv 3134 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wcel 2128   cdif 3099   wss 3102 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-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-dif 3104  df-in 3108  df-ss 3115 This theorem is referenced by:  sscond  3244  sbthlem1  6894  sbthlem2  6895
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