Theorem ss0 2303

Description: Any subset of the empty set is empty. Theorem 5 of [Suppes] p. 23.

Assertion

Ref	Expression
ss0	|- (A (_ (/) -> A = (/))

Proof of Theorem ss0

Step	Hyp	Ref	Expression
1		ss0b 2302	. 2 |- (A (_ (/) <-> A = (/))
2	1	biimp 151	1 |- (A (_ (/) -> A = (/))

Syntax hints:   -> wi 3   = wceq 956   (_ wss 2047  (/)c0 2280

This theorem is referenced by:  npss0 2309  ssdisj 2318  disjpss 2319  0dif 2336  fr0 2927  findsg 3157  tfindsg 3162  unixp0 3518  f00 3657  tz6.12-2 3739  map0b 4343  sbthlem7 4453  mapdom2lem 4493  phplem2 4509  rankeq0 4696  infxpidmlem11 7562  ntrcls0 7707  fgsb 10570  fgsbOLD 10571  fgsb2 10580

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-dif 2049  df-in 2051  df-ss 2053  df-nul 2281

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