Theorem oran 517

Description: Disjunction in terms of conjunction (De Morgan's law). Compare Theorem *4.57 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

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

Proof of Theorem oran

Step	Hyp	Ref	Expression
1		pm4.56 516	. 2 |- ( ( -. ph /\ -. ps ) <-> -. ( ph \/ ps ) )
2	1	con2bii 347	1 |- ( ( ph \/ ps ) <-> -. ( -. ph /\ -. ps ) )

Syntax hints:   -. wn 3   <-> wb 196   \/ wo 383   /\ wa 384

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 197  df-or 385  df-an 386

This theorem is referenced by:  pm4.57  518  19.43OLD  1811  ordthauslem  21187  mideulem2  25626  opphllem  25627  ordtconnlem1  29970  poimirlem9  33418  ftc1anclem1  33485  xrlttri5d  39495