Theorem pm5.21im 644

Description: Two propositions are equivalent if they are both false. Closed form of 2false 649. Equivalent to a bi2 128-like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013.) (Revised by Mario Carneiro, 31-Jan-2015.)

Assertion

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

Proof of Theorem pm5.21im

Step	Hyp	Ref	Expression
1		pm5.21 643	. 2 |- ( ( -. ph /\ -. ps ) -> ( ph <-> ps ) )
2	1	ex 113	1 |- ( -. ph -> ( -. ps -> ( ph <-> ps ) ) )

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

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 577

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  nbn2  645