Theorem nbn3 695

Description: Transfer falsehood via equivalence. (Contributed by NM, 11-Sep-2006.)

Hypothesis

Ref	Expression
nbn3.1	|- ph

Assertion

Ref	Expression
nbn3	|- ( -. ps <-> ( ps <-> -. ph ) )

Proof of Theorem nbn3

Step	Hyp	Ref	Expression
1		nbn3.1	. . 3 |- ph
2	1	notnoti 640	. 2 |- -. -. ph
3	2	nbn 694	1 |- ( -. ps <-> ( ps <-> -. ph ) )

Syntax hints:   -. wn 3   <-> wb 104

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 609  ax-in2 610

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)