Theorem pssirr 3603

Description: Proper subclass is irreflexive. Theorem 7 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.)

Assertion

Ref	Expression
pssirr

Proof of Theorem pssirr

Step	Hyp	Ref	Expression
1		pm3.24 882	. 2
2		dfpss3 3589	. 2
3	1, 2	mtbir 299	1

Syntax hints:  -.wn 3  /\wa 369  C_wss 3475  C.wpss 3476

This theorem is referenced by:  porpss  6584  ltsopr  9431

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ne 2654  df-in 3482  df-ss 3489  df-pss 3491