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Theorem ss0b 3284
 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 3283 . . 3
2 eqss 3015 . . 3
31, 2mpbiran2 883 . 2
43bicomi 130 1
 Colors of variables: wff set class Syntax hints:   wb 103   wceq 1285   wss 2974  c0 3252 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-dif 2976  df-in 2980  df-ss 2987  df-nul 3253 This theorem is referenced by:  ss0  3285  un00  3291  ssdisj  3301  pw0  3534  card0  6506
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