Theorem nbn 788

Description: The negation of a wff is equivalent to the wff's equivalence to falsehood.

Hypothesis

Ref	Expression
nbn.1	|- -. ph

Assertion

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

Proof of Theorem nbn

Step	Hyp	Ref	Expression
1		nbn.1	. . 3 |- -. ph
2		nbn2 787	. . 3 |- (-. ph -> (-. ps <-> (ph <-> ps)))
3	1, 2	ax-mp 7	. 2 |- (-. ps <-> (ph <-> ps))
4		bicom 576	. 2 |- ((ph <-> ps) <-> (ps <-> ph))
5	3, 4	bitri 189	1 |- (-. ps <-> (ps <-> ph))

Syntax hints:  -. wn 2   <-> wb 162

This theorem is referenced by:  nbn3 789  ne0f 2709  disj 2738  axnulALT 3258  dm0rn0 3986  reldm0 3987  intirrOLD 4124  falvar 13833

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 163  df-an 241

Copyright terms: Public domain