Theorem ss0 1727

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 1726	. 2 |- (A (_ (/) <-> A = (/))
2	1	biimp 133	1 |- (A (_ (/) -> A = (/))

Syntax hints:   -> wi 2   = wceq 1091   (_ wss 1487  (/)c0 1707

This theorem is referenced by:  npss0 1731  disjpss 1738  0dif 1757  uni0 1938  fr0 2179  findsg 2398  tfindsg 2402  f00 2773  tz6.12-2 2845  map0b 3267  sbthlem7 3355  mapdom2lem 3388  phplem3 3405  infxpidmlem11 4943

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-in 1491  df-ss 1492  df-nul 1708

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