Metamath Proof Explorer

Theorem neeq1

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

Ref Expression
Assertion neeq1 
|- ( A = B -> ( A =/= C <-> B =/= C ) )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( A = B -> A = B )
2 1 neeq1d 
 |-  ( A = B -> ( A =/= C <-> B =/= C ) )