Theorem bj-nnor 13615

Description: Double negation of a disjunction in terms of implication. (Contributed by BJ, 9-Oct-2019.)

Assertion

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

Proof of Theorem bj-nnor

Step	Hyp	Ref	Expression
1		ioran 742	. . 3 |- ( -. ( ph \/ ps ) <-> ( -. ph /\ -. ps ) )
2	1	notbii 658	. 2 |- ( -. -. ( ph \/ ps ) <-> -. ( -. ph /\ -. ps ) )
3		imnan 680	. 2 |- ( ( -. ph -> -. -. ps ) <-> -. ( -. ph /\ -. ps ) )
4	2, 3	bitr4i 186	1 |- ( -. -. ( ph \/ ps ) <-> ( -. ph -> -. -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103   <-> wb 104   \/ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  bj-nndcALT  13639