Metamath Proof Explorer


Theorem con2d

Description: A contraposition deduction. (Contributed by NM, 19-Aug-1993)

Ref Expression
Hypothesis con2d.1
|- ( ph -> ( ps -> -. ch ) )
Assertion con2d
|- ( ph -> ( ch -> -. ps ) )

Proof

Step Hyp Ref Expression
1 con2d.1
 |-  ( ph -> ( ps -> -. ch ) )
2 notnotr
 |-  ( -. -. ps -> ps )
3 2 1 syl5
 |-  ( ph -> ( -. -. ps -> -. ch ) )
4 3 con4d
 |-  ( ph -> ( ch -> -. ps ) )