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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 )