Theorem pm4.52 477

Description: Theorem *4.52 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)

Assertion

Ref	Expression
pm4.52	|- ((ph /\ -. ps) <-> -. (-. ph \/ ps))

Proof of Theorem pm4.52

Step	Hyp	Ref	Expression
1		annim 414	. 2 |- ((ph /\ -. ps) <-> -. (ph -> ps))
2		imor 401	. 2 |- ((ph -> ps) <-> (-. ph \/ ps))
3	1, 2	xchbinx 301	1 |- ((ph /\ -. ps) <-> -. (-. ph \/ ps))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is used by:  pm4.53  478