Theorem pm4.83 742

Description: Theorem *4.83 of [WhiteheadRussell] p. 122.

Assertion

Ref	Expression
pm4.83	|- (((ph -> ps) /\ (-. ph -> ps)) <-> ps)

Proof of Theorem pm4.83

Step	Hyp	Ref	Expression
1		exmid 657	. . 3 |- (ph \/ -. ph)
2	1	a1bi 197	. 2 |- (ps <-> ((ph \/ -. ph) -> ps))
3		jaob 424	. 2 |- (((ph \/ -. ph) -> ps) <-> ((ph -> ps) /\ (-. ph -> ps)))
4	2, 3	bitr2 174	1 |- (((ph -> ps) /\ (-. ph -> ps)) <-> ps)

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222   /\ wa 223

This theorem is referenced by:  ivthlem6 7286  dmdbr5at 10344

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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