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 ) )