Theorem pssirr 2136

Description: Proper subclass is irreflexive. Theorem 7 of [Suppes] p. 23.

Assertion

Ref	Expression
pssirr	|- -. A (. A

Proof of Theorem pssirr

Step	Hyp	Ref	Expression
1		pm3.24 656	. 2 |- -. (A (_ A /\ -. A (_ A)
2		dfpss3 2124	. 2 |- (A (. A <-> (A (_ A /\ -. A (_ A))
3	1, 2	mtbir 192	1 |- -. A (. A

Syntax hints:  -. wn 2   /\ wa 223   (_ wss 2037   (. wpss 2038

This theorem is referenced by:  ssnpss 2139  zorn 4769  ltsopr 5108

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-in 2041  df-ss 2043  df-pss 2045

Copyright terms: Public domain