Theorem pm5.21ni 651

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

Hypotheses

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

Assertion

Ref	Expression
pm5.21ni	|- ( -. ps -> ( ph <-> ch ) )

Proof of Theorem pm5.21ni

Step	Hyp	Ref	Expression
1		pm5.21ni.1	. . 3 |- ( ph -> ps )
2	1	con3i 594	. 2 |- ( -. ps -> -. ph )
3		pm5.21ni.2	. . 3 |- ( ch -> ps )
4	3	con3i 594	. 2 |- ( -. ps -> -. ch )
5	2, 4	2falsed 650	1 |- ( -. ps -> ( ph <-> ch ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  niabn  908