Theorem pssirrOLD 4060

Description: Obsolete version of pssirr 4059 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		pm3.24 407	. 2 ⊢ ¬ (𝐴 ⊆ 𝐴 ∧ ¬ 𝐴 ⊆ 𝐴)
2		dfpss3 4045	. 2 ⊢ (𝐴 ⊊ 𝐴 ↔ (𝐴 ⊆ 𝐴 ∧ ¬ 𝐴 ⊆ 𝐴))
3	1, 2	mtbir 326	1 ⊢ ¬ 𝐴 ⊊ 𝐴

Syntax hints:  ¬ wn 3   ∧ wa 400   ⊆ wss 3907   ⊊ 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-ss 3924  df-pss 3927

This theorem is referenced by: (None)