Theorem pssirr 4059

Description: Proper subclass is irreflexive. Theorem 7 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026.)

Assertion

Ref	Expression
pssirr	⊢ ¬ 𝐴 ⊊ 𝐴

Proof of Theorem pssirr

Step	Hyp	Ref	Expression
1		neirr 2969	. 2 ⊢ ¬ 𝐴 ≠ 𝐴
2		pssne 4055	. 2 ⊢ (𝐴 ⊊ 𝐴 → 𝐴 ≠ 𝐴)
3	1, 2	mto 200	1 ⊢ ¬ 𝐴 ⊊ 𝐴

Syntax hints:  ¬ wn 3   ≠ wne 2960   ⊊ wpss 3908

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1803  df-cleq 2757  df-ne 2961  df-pss 3927

This theorem is referenced by:  porpss  7714  ltsopr  11005