Theorem pm4.54 514

Description: Theorem *4.54 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)

Assertion

Ref	Expression
pm4.54	|- ( ( -. ph /\ ps ) <-> -. ( ph \/ -. ps ) )

Proof of Theorem pm4.54

Step	Hyp	Ref	Expression
1		df-an 386	. 2 |- ( ( -. ph /\ ps ) <-> -. ( -. ph -> -. ps ) )
2		pm4.66 436	. 2 |- ( ( -. ph -> -. ps ) <-> ( ph \/ -. ps ) )
3	1, 2	xchbinx 324	1 |- ( ( -. ph /\ ps ) <-> -. ( ph \/ -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383   /\ wa 384

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  df-or 385  df-an 386

This theorem is referenced by:  pm4.55  515