Theorem norbi 904

Description: If neither of two propositions is true, then these propositions are equivalent. (Contributed by BJ, 26-Apr-2019.)

Assertion

Ref	Expression
norbi	|- ( -. ( ph \/ ps ) -> ( ph <-> ps ) )

Proof of Theorem norbi

Step	Hyp	Ref	Expression
1		orc 400	. 2 |- ( ph -> ( ph \/ ps ) )
2		olc 399	. 2 |- ( ps -> ( ph \/ ps ) )
3	1, 2	pm5.21ni 367	1 |- ( -. ( ph \/ ps ) -> ( ph <-> ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383

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  df-or 385

This theorem is referenced by:  nbior  905  oibabs  925