Theorem bj-nnim 13770

Description: The double negation of an implication implies the implication with the consequent doubly negated. (Contributed by BJ, 24-Nov-2023.)

Assertion

Ref	Expression
bj-nnim	|- ( -. -. ( ph -> ps ) -> ( ph -> -. -. ps ) )

Proof of Theorem bj-nnim

Step	Hyp	Ref	Expression
1		jcn 646	. 2 |- ( ph -> ( -. ps -> -. ( ph -> ps ) ) )
2	1	con3rr3 628	1 |- ( -. -. ( ph -> ps ) -> ( ph -> -. -. ps ) )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 609  ax-in2 610

This theorem is referenced by:  bj-stim  13781