Theorem ioran 476

Description: Negated disjunction in terms of conjunction (De Morgan's law). Compare Theorem *4.56 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

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

Proof of Theorem ioran

Step	Hyp	Ref	Expression
1		pm4.65 416	. 2 |- (-. (-. ph -> ps) <-> (-. ph /\ -. ps))
2		pm4.64 361	. 2 |- ((-. ph -> ps) <-> (ph \/ ps))
3	1, 2	xchnxbi 299	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:  pm4.56  481  oibabs  851  xor  861  3ioran  950  3ori  1242  ecase23d  1285  19.43OLD  1606  equvini  1987  2ralor  2781  dfun2  3491  sfin111  4537  nchoice  6309