Theorem pm4.15 353

Description: Theorem *4.15 of [WhiteheadRussell] p. 117.

Assertion

Ref	Expression
pm4.15	|- (((ph /\ ps) -> -. ch) <-> ((ps /\ ch) -> -. ph))

Proof of Theorem pm4.15

Step	Hyp	Ref	Expression
1		impexp 347	. 2 |- (((ph /\ ps) -> -. ch) <-> (ph -> (ps -> -. ch)))
2		imnan 242	. . 3 |- ((ps -> -. ch) <-> -. (ps /\ ch))
3	2	imbi2i 185	. 2 |- ((ph -> (ps -> -. ch)) <-> (ph -> -. (ps /\ ch)))
4		bi2.03 165	. 2 |- ((ph -> -. (ps /\ ch)) <-> ((ps /\ ch) -> -. ph))
5	1, 3, 4	3bitr 177	1 |- (((ph /\ ps) -> -. ch) <-> ((ps /\ ch) -> -. ph))

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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