Theorem pssne

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

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

Proof

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