Theorem anor 304

Description: Conjunction in terms of disjunction (DeMorgan's law). Theorem *4.5 of [WhiteheadRussell] p. 120.

Assertion

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

Proof of Theorem anor

Step	Hyp	Ref	Expression
1		df-an 225	. 2 |- ((ph /\ ps) <-> -. (ph -> -. ps))
2		pm4.62 235	. . 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   -> wi 3   <-> wb 146   \/ wo 222   /\ wa 223

This theorem is referenced by:  ianor 305  ioran 306  pm4.52 307  pm4.54 309  pm3.1 314  pm3.11 315  andi 603

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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