Theorem pm4.14 352

Description: Theorem *4.14 of [WhiteheadRussell] p. 117.

Assertion

Ref	Expression
pm4.14	|- (((ph /\ ps) -> ch) <-> ((ph /\ -. ch) -> -. ps))

Proof of Theorem pm4.14

Step	Hyp	Ref	Expression
1		impexp 347	. . 3 |- (((ph /\ ps) -> ch) <-> (ph -> (ps -> ch)))
2		bi2.04 160	. . 3 |- ((ph -> (ps -> ch)) <-> (ps -> (ph -> ch)))
3	1, 2	bitr 173	. 2 |- (((ph /\ ps) -> ch) <-> (ps -> (ph -> ch)))
4		iman 237	. . 3 |- ((ph -> ch) <-> -. (ph /\ -. ch))
5	4	imbi2i 185	. 2 |- ((ps -> (ph -> ch)) <-> (ps -> -. (ph /\ -. ch)))
6		bi2.03 165	. 2 |- ((ps -> -. (ph /\ -. ch)) <-> ((ph /\ -. ch) -> -. ps))
7	3, 5, 6	3bitr 177	1 |- (((ph /\ ps) -> ch) <-> ((ph /\ -. ch) -> -. ps))

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

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-an 225

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