Theorem oran 255

Description: Disjunction in terms of conjunction (DeMorgan's law). Compare Theorem *4.57 of [WhiteheadRussell] p. 120.

Assertion

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

Proof of Theorem oran

Step	Hyp	Ref	Expression
1		pm4.13 142	. 2 |- ((ph \/ ps) <-> -. -. (ph \/ ps))
2		ioran 254	. . 3 |- (-. (ph \/ ps) <-> (-. ph /\ -. ps))
3	2	negbii 162	. 2 |- (-. -. (ph \/ ps) <-> -. (-. ph /\ -. ps))
4	1, 3	bitr 151	1 |- ((ph \/ ps) <-> -. (-. ph /\ -. ps))

Syntax hints:  -. wn 1   <-> wb 127   \/ wo 195   /\ wa 196

This theorem is referenced by:  orim12i 271  jao 274  andi 456  19.43 767  dmsnsn0 2544  mdsym 5784

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198

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