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Metamath Proof Explorer

Theorem con1bid

Description: A contraposition deduction. (Contributed by NM, 9-Oct-1999)

Ref Expression
Hypothesis con1bid.1 
|- ( ph -> ( -. ps <-> ch ) )
Assertion con1bid 
|- ( ph -> ( -. ch <-> ps ) )

Proof

Step Hyp Ref Expression
1 con1bid.1 
 |-  ( ph -> ( -. ps <-> ch ) )
2 1 bicomd 
 |-  ( ph -> ( ch <-> -. ps ) )
3 2 con2bid 
 |-  ( ph -> ( ps <-> -. ch ) )
4 3 bicomd 
 |-  ( ph -> ( -. ch <-> ps ) )