Theorem pm4.79 355

Description: Theorem *4.79 of [WhiteheadRussell] p. 121.

Assertion

Ref	Expression
pm4.79	|- (((ps -> ph) \/ (ch -> ph)) <-> ((ps /\ ch) -> ph))

Proof of Theorem pm4.79

Step	Hyp	Ref	Expression
1		pm4.78 354	. . 3 |- (((-. ph -> -. ps) \/ (-. ph -> -. ch)) <-> (-. ph -> (-. ps \/ -. ch)))
2		ianor 305	. . . 4 |- (-. (ps /\ ch) <-> (-. ps \/ -. ch))
3	2	imbi2i 185	. . 3 |- ((-. ph -> -. (ps /\ ch)) <-> (-. ph -> (-. ps \/ -. ch)))
4	1, 3	bitr4 176	. 2 |- (((-. ph -> -. ps) \/ (-. ph -> -. ch)) <-> (-. ph -> -. (ps /\ ch)))
5		pm4.1 164	. . 3 |- ((ps -> ph) <-> (-. ph -> -. ps))
6		pm4.1 164	. . 3 |- ((ch -> ph) <-> (-. ph -> -. ch))
7	5, 6	orbi12i 257	. 2 |- (((ps -> ph) \/ (ch -> ph)) <-> ((-. ph -> -. ps) \/ (-. ph -> -. ch)))
8		pm4.1 164	. 2 |- (((ps /\ ch) -> ph) <-> (-. ph -> -. (ps /\ ch)))
9	4, 7, 8	3bitr4 183	1 |- (((ps -> ph) \/ (ch -> ph)) <-> ((ps /\ ch) -> ph))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222   /\ 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-or 224  df-an 225

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