Metamath Proof Explorer


Theorem necon3i

Description: Contrapositive inference for inequality. (Contributed by NM, 9-Aug-2006) (Proof shortened by Wolf Lammen, 22-Nov-2019)

Ref Expression
Hypothesis necon3i.1
|- ( A = B -> C = D )
Assertion necon3i
|- ( C =/= D -> A =/= B )

Proof

Step Hyp Ref Expression
1 necon3i.1
 |-  ( A = B -> C = D )
2 1 necon3ai
 |-  ( C =/= D -> -. A = B )
3 2 neqned
 |-  ( C =/= D -> A =/= B )