Theorem bj-nnor 14626

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 752	. . 3 |- ( -. ( ph \/ ps ) <-> ( -. ph /\ -. ps ) )
2	1	notbii 668	. 2 |- ( -. -. ( ph \/ ps ) <-> -. ( -. ph /\ -. ps ) )
3		imnan 690	. 2 |- ( ( -. ph -> -. -. ps ) <-> -. ( -. ph /\ -. ps ) )
4	2, 3	bitr4i 187	1 |- ( -. -. ( ph \/ ps ) <-> ( -. ph -> -. -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   <-> wb 105   \/ wo 708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  bj-nndcALT  14650