Theorem pm5.21im 364

Description: Two propositions are equivalent if they are both false. Closed form of 2false 365. Equivalent to a biimpr 210-like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013.)

Assertion

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

Proof of Theorem pm5.21im

Step	Hyp	Ref	Expression
1		nbn2 360	. 2 |- ( -. ph -> ( -. ps <-> ( ph <-> ps ) ) )
2	1	biimpd 219	1 |- ( -. ph -> ( -. ps -> ( ph <-> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  pm5.21ndd  369  pm5.21  903