Metamath Proof Explorer


Theorem neeq2

Description: Equality theorem for inequality. (Contributed by NM, 19-Nov-1994) (Proof shortened by Wolf Lammen, 18-Nov-2019)

Ref Expression
Assertion neeq2 ( 𝐴 = 𝐵 → ( 𝐶𝐴𝐶𝐵 ) )

Proof

Step Hyp Ref Expression
1 id ( 𝐴 = 𝐵𝐴 = 𝐵 )
2 1 neeq2d ( 𝐴 = 𝐵 → ( 𝐶𝐴𝐶𝐵 ) )