Theorem pssssd 3367

Description: Deduce subclass from proper subclass. (Contributed by NM, 29-Feb-1996.)

Hypothesis

Ref	Expression
pssssd.1	⊢ (φ → A ⊊ B)

Assertion

Ref	Expression
pssssd	⊢ (φ → A ⊆ B)

Proof of Theorem pssssd

Step	Hyp	Ref	Expression
1		pssssd.1	. 2 ⊢ (φ → A ⊊ B)
2		pssss 3365	. 2 ⊢ (A ⊊ B → A ⊆ B)
3	1, 2	syl 15	1 ⊢ (φ → A ⊆ B)

This proof depends on syntax axioms:   → wi 4   ⊆ wss 3258   ⊊ wpss 3259

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  sfinltfin  4536