Theorem pssirr 3370

Description: Proper subclass is irreflexive. Theorem 7 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.)

Assertion

Ref	Expression
pssirr	⊢ ¬ A ⊊ A

Proof of Theorem pssirr

Step	Hyp	Ref	Expression
1		pm3.24 852	. 2 ⊢ ¬ (A ⊆ A ∧ ¬ A ⊆ A)
2		dfpss3 3356	. 2 ⊢ (A ⊊ A ↔ (A ⊆ A ∧ ¬ A ⊆ A))
3	1, 2	mtbir 290	1 ⊢ ¬ A ⊊ A

Syntax hints:  ¬ wn 3   ∧ wa 358   ⊆ wss 3258   ⊊ wpss 3259

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-ne 2519  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-ss 3260  df-pss 3262

This theorem is referenced by: (None)