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Metamath Proof Explorer

Theorem neeq1i

Description: Inference for inequality. (Contributed by NM, 29-Apr-2005) (Proof shortened by Wolf Lammen, 19-Nov-2019)

Ref Expression
Hypothesis neeq1i.1 ⊢ A = B
Assertion neeq1i ⊢ A ≠ C ↔ B ≠ C

Proof

Step Hyp Ref Expression
1 neeq1i.1 ⊢ A = B
2 1 eqeq1i ⊢ A = C ↔ B = C
3 2 necon3bii ⊢ A ≠ C ↔ B ≠ C