Metamath Proof Explorer

Theorem necon1ai

Description: Contrapositive inference for inequality. (Contributed by NM, 12-Feb-2007) (Proof shortened by Wolf Lammen, 22-Nov-2019)

Ref Expression
Hypothesis necon1ai.1 
|- ( -. ph -> A = B )
Assertion necon1ai 
|- ( A =/= B -> ph )

Proof

Step Hyp Ref Expression
1 necon1ai.1 
 |-  ( -. ph -> A = B )
2 1 necon3ai 
 |-  ( A =/= B -> -. -. ph )
3 2 notnotrd 
 |-  ( A =/= B -> ph )