Metamath Proof Explorer

Theorem con1b

Description: Contraposition. Bidirectional version of con1 . (Contributed by NM, 3-Jan-1993)

Ref Expression
Assertion con1b 
|- ( ( -. ph -> ps ) <-> ( -. ps -> ph ) )

Proof

Step Hyp Ref Expression
1 con1 
 |-  ( ( -. ph -> ps ) -> ( -. ps -> ph ) )
2 con1 
 |-  ( ( -. ps -> ph ) -> ( -. ph -> ps ) )
3 1 2 impbii 
 |-  ( ( -. ph -> ps ) <-> ( -. ps -> ph ) )