Theorem nbbn 373

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 372	. 2 |- ( -. ( ph <-> ps ) <-> ( ph <-> -. ps ) )
2		con2bi 343	. 2 |- ( ( ph <-> -. ps ) <-> ( ps <-> -. ph ) )
3		bicom 212	. 2 |- ( ( ps <-> -. ph ) <-> ( -. ph <-> ps ) )
4	1, 2, 3	3bitrri 287	1 |- ( ( -. ph <-> ps ) <-> -. ( ph <-> ps ) )

Syntax hints:   -. wn 3   <-> wb 196

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 197

This theorem is referenced by:  biass  374  pclem6  971  xorass  1468  hadbi  1537  canth  6608  qextltlem  12033  onint1  32448  notbinot1  33878  notbinot2  33882