Theorem oranim 851

Description: Disjunction in terms of conjunction (DeMorgan's law). One direction of Theorem *4.57 of [WhiteheadRussell] p. 120. The converse does not hold intuitionistically but does hold in classical logic. (Contributed by Jim Kingdon, 25-Jul-2018.)

Assertion

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

Proof of Theorem oranim

Step	Hyp	Ref	Expression
1		pm4.56 850	. . 3 |- ( ( -. ph /\ -. ps ) <-> -. ( ph \/ ps ) )
2	1	biimpi 119	. 2 |- ( ( -. ph /\ -. ps ) -> -. ( ph \/ ps ) )
3	2	con2i 597	1 |- ( ( ph \/ ps ) -> -. ( -. ph /\ -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103   \/ wo 670

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585  ax-io 671

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  unssin  3262  prneimg  3648  ftpg  5536  xrlttri3  9424