Theorem pm4.54 309

Description: Theorem *4.54 of [WhiteheadRussell] p. 120.

Assertion

Ref	Expression
pm4.54	|- ((-. ph /\ ps) <-> -. (ph \/ -. ps))

Proof of Theorem pm4.54

Step	Hyp	Ref	Expression
1		anor 304	. 2 |- ((-. ph /\ ps) <-> -. (-. -. ph \/ -. ps))
2		pm4.13 161	. . . 4 |- (ph <-> -. -. ph)
3	2	orbi1i 256	. . 3 |- ((ph \/ -. ps) <-> (-. -. ph \/ -. ps))
4	3	negbii 187	. 2 |- (-. (ph \/ -. ps) <-> -. (-. -. ph \/ -. ps))
5	1, 4	bitr4 176	1 |- ((-. ph /\ ps) <-> -. (ph \/ -. ps))

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

This theorem is referenced by:  pm4.55 310

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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