Metamath Proof Explorer

Theorem con2b

Description: Contraposition. Bidirectional version of con2 . (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion con2b 
|- ( ( ph -> -. ps ) <-> ( ps -> -. ph ) )

Proof

Step Hyp Ref Expression
1 con2 
 |-  ( ( ph -> -. ps ) -> ( ps -> -. ph ) )
2 con2 
 |-  ( ( ps -> -. ph ) -> ( ph -> -. ps ) )
3 1 2 impbii 
 |-  ( ( ph -> -. ps ) <-> ( ps -> -. ph ) )