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Theorem 0pss 2298

Description: The null set is a proper subset of any non-empty set.

Assertion

Ref	Expression
0pss

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Proof of Theorem 0pss

Step	Hyp	Ref	Expression
1		df-pss 2045	. . 3
2		0ss 2291	. . 3
3	1, 2	mpbiran 726	. 2
4		necom 1628	. 2
5	3, 4	bitr 173	1

Colors of variables: wff set class

Syntax hints:   wb 146   wne 1577   wss 2037   wpss 2038  c0 2270

This theorem is referenced by:  npss0 2299  php 4493  prn0 5065  genpn0 5078  1pr 5089  ltexprlem5 5118  reclem1pr 5128  suplem1pr 5133  infxpidmlem10 7504

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-ne 1579  df-v 1803  df-dif 2039  df-in 2041  df-ss 2043  df-pss 2045  df-nul 2271

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