Theorem pm4.54 479

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 360	. 2 |- ((-. ph /\ ps) <-> -. (-. ph -> -. ps))
2		pm4.66 409	. 2 |- ((-. ph -> -. ps) <-> (ph \/ -. ps))
3	1, 2	xchbinx 301	1 |- ((-. ph /\ ps) <-> -. (ph \/ -. ps))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357   /\ wa 358

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 177  df-or 359  df-an 360

This theorem is referenced by:  pm4.55  480