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Metamath Proof Explorer

Theorem pm5.21ni

Description: Two propositions implying a false one are equivalent. (Contributed by NM, 16-Feb-1996) (Proof shortened by Wolf Lammen, 19-May-2013)

Ref Expression
Hypotheses pm5.21ni.1 
|- ( ph -> ps )
pm5.21ni.2 
|- ( ch -> ps )
Assertion pm5.21ni 
|- ( -. ps -> ( ph <-> ch ) )

Proof

Step Hyp Ref Expression
1 pm5.21ni.1 
 |-  ( ph -> ps )
2 pm5.21ni.2 
 |-  ( ch -> ps )
3 1 con3i 
 |-  ( -. ps -> -. ph )
4 2 con3i 
 |-  ( -. ps -> -. ch )
5 3 4 2falsed 
 |-  ( -. ps -> ( ph <-> ch ) )