Theorem ss0 2299

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 2298	. 2 |- (A (_ (/) <-> A = (/))
2	1	biimp 151	1 |- (A (_ (/) -> A = (/))

Syntax hints:   -> wi 3   = wceq 954   (_ wss 2043  (/)c0 2276

This theorem is referenced by:  npss0 2305  ssdisj 2314  disjpss 2315  0dif 2332  fr0 2922  findsg 3152  tfindsg 3157  unixp0 3510  f00 3648  tz6.12-2 3730  map0b 4333  sbthlem7 4439  mapdom2lem 4479  phplem2 4495  rankeq0 4676  infxpidmlem11 7513  ntrcls0 7657  fgsb 10480  fgsb2 10485

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-v 1808  df-dif 2045  df-in 2047  df-ss 2049  df-nul 2277

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