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Metamath Proof Explorer

Theorem ltnei

Description: 'Less than' implies not equal. (Contributed by NM, 28-Jul-1999)

Ref Expression
Hypotheses lt.1 ⊢ A ∈ ℝ
lt.2 ⊢ B ∈ ℝ
Assertion ltnei ⊢ A < B → B ≠ A

Proof

Step Hyp Ref Expression
1 lt.1 ⊢ A ∈ ℝ
2 lt.2 ⊢ B ∈ ℝ
3 ltne ⊢ A ∈ ℝ ∧ A < B → B ≠ A
4 1 3 mpan ⊢ A < B → B ≠ A