Theorem pssirrOLD 4057

Description: Obsolete version of pssirr 4056 as of 10-Jun-2026. (Contributed by NM, 7-Feb-1996.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
pssirrOLD	⊢ ¬ 𝐴 ⊊ 𝐴

Proof of Theorem pssirrOLD

Step	Hyp	Ref	Expression
1		pm3.24 406	. 2 ⊢ ¬ (𝐴 ⊆ 𝐴 ∧ ¬ 𝐴 ⊆ 𝐴)
2		dfpss3 4042	. 2 ⊢ (𝐴 ⊊ 𝐴 ↔ (𝐴 ⊆ 𝐴 ∧ ¬ 𝐴 ⊆ 𝐴))
3	1, 2	mtbir 325	1 ⊢ ¬ 𝐴 ⊊ 𝐴

Syntax hints:  ¬ wn 3   ∧ wa 399   ⊆ wss 3904   ⊊ wpss 3905

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1799  df-cleq 2753  df-ne 2957  df-ss 3921  df-pss 3924

This theorem is referenced by: (None)