This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem neeq2i

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 neeq2i ⊢ C ≠ A ↔ C ≠ B

Proof

Step Hyp Ref Expression
1 neeq1i.1 ⊢ A = B
2 1 eqeq2i ⊢ C = A ↔ C = B
3 2 necon3bii ⊢ C ≠ A ↔ C ≠ B