Theorem pssne 3366

Description: Two classes in a proper subclass relationship are not equal. (Contributed by NM, 16-Feb-2015.)

Assertion

Ref	Expression
pssne	⊢ (A ⊊ B → A ≠ B)

Proof of Theorem pssne

Step	Hyp	Ref	Expression
1		df-pss 3262	. 2 ⊢ (A ⊊ B ↔ (A ⊆ B ∧ A ≠ B))
2	1	simprbi 450	1 ⊢ (A ⊊ B → A ≠ B)

This proof depends on syntax axioms:   → wi 4   ≠ wne 2517   ⊆ 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:  pssned  3368