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Theorem ss0 3285
Description: Any subset of the empty set is empty. Theorem 5 of [Suppes] p. 23. (Contributed by NM, 13-Aug-1994.)
Assertion
Ref Expression
ss0  |-  ( A 
C_  (/)  ->  A  =  (/) )

Proof of Theorem ss0
StepHypRef Expression
1 ss0b 3284 . 2  |-  ( A 
C_  (/)  <->  A  =  (/) )
21biimpi 118 1  |-  ( A 
C_  (/)  ->  A  =  (/) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285    C_ 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:  sseq0  3286  abf  3288  eq0rdv  3289  ssdisj  3301  0dif  3316  poirr2  4741  iotanul  4906  f00  5106  phplem2  6378  php5dom  6388  ixxdisj  8991  icodisj  9079  ioodisj  9080  uzdisj  9175  nn0disj  9214
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