Theorem pssne 3040

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 2933	. 2 ⊢ (𝐴 ⊊ 𝐵 ↔ (𝐴 ⊆ 𝐵 ∧ 𝐴 ≠ 𝐵))
2	1	simprbi 260	1 ⊢ (𝐴 ⊊ 𝐵 → 𝐴 ≠ 𝐵)

Syntax hints:   → wi 4   ≠ wne 2204   ⊆ wss 2917   ⊊ wpss 2918

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100

This theorem depends on definitions:  df-bi 110  df-pss 2933

This theorem is referenced by:  pssned  3042