Theorem pssirr 4030

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 2964	. 2 ⊢ ¬ 𝐴 ≠ 𝐴
2		pssne 4026	. 2 ⊢ (𝐴 ⊊ 𝐴 → 𝐴 ≠ 𝐴)
3	1, 2	mto 200	1 ⊢ ¬ 𝐴 ⊊ 𝐴

This proof depends on syntax axioms:  ¬ wn 3   ≠ wne 2955   ⊊ wpss 4013

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-cleq 2752  df-ne 2956  df-pss 4014

This theorem is used by:  porpss  7743  ltsopr  11120