Theorem pssirr 4032

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

Assertion

Ref	Expression
pssirr	⊢ ¬ 𝐴 ⊊ 𝐴

Proof of Theorem pssirr

Step	Hyp	Ref	Expression
1		pm3.24 406	. 2 ⊢ ¬ (𝐴 ⊆ 𝐴 ∧ ¬ 𝐴 ⊆ 𝐴)
2		dfpss3 4018	. 2 ⊢ (𝐴 ⊊ 𝐴 ↔ (𝐴 ⊆ 𝐴 ∧ ¬ 𝐴 ⊆ 𝐴))
3	1, 2	mtbir 326	1 ⊢ ¬ 𝐴 ⊊ 𝐴

Syntax hints:  ¬ wn 3   ∧ wa 399   ⊆ wss 3884   ⊊ wpss 3885

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2114  ax-9 2122  ax-ext 2710

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-ex 1788  df-sb 2073  df-clab 2717  df-cleq 2731  df-clel 2818  df-ne 2944  df-v 3425  df-in 3891  df-ss 3901  df-pss 3903

This theorem is referenced by:  porpss  7555  ltsopr  10694