Theorem pssss 3365

Description: A proper subclass is a subclass. Theorem 10 of [Suppes] p. 23. (Contributed by NM, 7-Feb-1996.)

Assertion

Ref	Expression
pssss	⊢ (A ⊊ B → A ⊆ B)

Proof of Theorem pssss

Step	Hyp	Ref	Expression
1		df-pss 3262	. 2 ⊢ (A ⊊ B ↔ (A ⊆ B ∧ A ≠ B))
2	1	simplbi 446	1 ⊢ (A ⊊ B → A ⊆ B)

Syntax hints:   → wi 4   ≠ wne 2517   ⊆ wss 3258   ⊊ wpss 3259

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-pss 3262

This theorem is referenced by:  pssssd  3367  sspss  3369  pssn2lp  3371  psstr  3374