Theorem pssirrOLD 4055

Description: Obsolete version of pssirr 4054 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		pm3.24 408	. 2 ⊢ ¬ (𝐴 ⊆ 𝐴 ∧ ¬ 𝐴 ⊆ 𝐴)
2		dfpss3 4040	. 2 ⊢ (𝐴 ⊊ 𝐴 ↔ (𝐴 ⊆ 𝐴 ∧ ¬ 𝐴 ⊆ 𝐴))
3	1, 2	mtbir 326	1 ⊢ ¬ 𝐴 ⊊ 𝐴

This proof depends on syntax axioms:  ¬ wn 3   ∧ wa 401   ⊆ wss 3902   ⊊ wpss 3903

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 2155  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2754  df-ne 2958  df-ss 3919  df-pss 3922

This theorem is used by: (None)