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Theorem ss0b 3402
 Description: Any subset of the empty set is empty. Theorem 5 of [Suppes] p. 23 and its converse. (Contributed by NM, 17-Sep-2003.)
Assertion
Ref Expression
ss0b

Proof of Theorem ss0b
StepHypRef Expression
1 0ss 3401 . . 3
2 eqss 3112 . . 3
31, 2mpbiran2 925 . 2
43bicomi 131 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1331   wss 3071  c0 3363 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 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-dif 3073  df-in 3077  df-ss 3084  df-nul 3364 This theorem is referenced by:  ss0  3403  un00  3409  ssdisj  3419  pw0  3667  card0  7044  0nnei  12322
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