Theorem nbbn 359

Description: Move negation outside of biconditional. Compare Theorem *5.18 of [WhiteheadRussell] p. 124. (Contributed by NM, 27-Jun-2002.) (Proof shortened by Wolf Lammen, 20-Sep-2013.)

Assertion

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

Proof of Theorem nbbn

Step	Hyp	Ref	Expression
1		xor3 358	. 2 |- ( -. ( ph <-> ps ) <-> ( ph <-> -. ps ) )
2		con2bi 329	. 2 |- ( ( ph <-> -. ps ) <-> ( ps <-> -. ph ) )
3		bicom 203	. 2 |- ( ( ps <-> -. ph ) <-> ( -. ph <-> ps ) )
4	1, 2, 3	3bitrri 275	1 |- ( ( -. ph <-> ps ) <-> -. ( ph <-> ps ) )

Syntax hints:   -. wn 3   <-> wb 187

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 188

This theorem is referenced by:  biass  360  pclem6  938  xorass  1404  xorassOLD  1405  xorneg1OLD  1413  trubifalOLD  1478  hadbi  1496  canth  6255  qextltlem  11484  onint1  30935  notbinot1  32060  notbinot2  32064