Metamath Proof Explorer


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