Metamath Proof Explorer

Theorem necon1bbii

Description: Contrapositive inference for inequality. (Contributed by NM, 17-Mar-2007) (Proof shortened by Wolf Lammen, 24-Nov-2019)

Ref Expression
Hypothesis necon1bbii.1 
|- ( A =/= B <-> ph )
Assertion necon1bbii 
|- ( -. ph <-> A = B )

Proof

Step Hyp Ref Expression
1 necon1bbii.1 
 |-  ( A =/= B <-> ph )
2 nne 
 |-  ( -. A =/= B <-> A = B )
3 2 1 xchnxbi 
 |-  ( -. ph <-> A = B )