Theorem pssirr 4060

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 2970	. 2 ⊢ ¬ 𝐴 ≠ 𝐴
2		pssne 4056	. 2 ⊢ (𝐴 ⊊ 𝐴 → 𝐴 ≠ 𝐴)
3	1, 2	mto 200	1 ⊢ ¬ 𝐴 ⊊ 𝐴

This proof depends on syntax axioms:  ¬ wn 3   ≠ wne 2961   ⊊ wpss 3909

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-9 2156  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2758  df-ne 2962  df-pss 3928

This theorem is used by:  porpss  7737  ltsopr  11035