Theorem oran 312

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		pm4.13 161	. 2 |- ((ph \/ ps) <-> -. -. (ph \/ ps))
2		ioran 306	. . 3 |- (-. (ph \/ ps) <-> (-. ph /\ -. ps))
3	2	negbii 187	. 2 |- (-. -. (ph \/ ps) <-> -. (-. ph /\ -. ps))
4	1, 3	bitr 173	1 |- ((ph \/ ps) <-> -. (-. ph /\ -. ps))

Syntax hints:  -. wn 2   <-> wb 146   \/ wo 222   /\ wa 223

This theorem is referenced by:  pm4.57 313  orim12i 336  jao 340  andi 604  xor2 673  19.43 1088  rexpr 2429  dmsnsn0 3325

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

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