Theorem oranim 793

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		pm4.56 792	. . 3 |- ( ( -. ph /\ -. ps ) <-> -. ( ph \/ ps ) )
2	1	biimpi 120	. 2 |- ( ( -. ph /\ -. ps ) -> -. ( ph \/ ps ) )
3	2	con2i 636	1 |- ( ( ph \/ ps ) -> -. ( -. ph /\ -. ps ) )

This proof depends on syntax axioms:   -. wn 3   -> wi 4   /\ wa 104   \/ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  unssin  3470  prneimg  3899  ftpg  5899  xrlttri3  10199