Theorem pm5.6 686

Description: Conjunction in antecedent versus disjunction in consequent. Theorem *5.6 of [WhiteheadRussell] p. 125.

Assertion

Ref	Expression
pm5.6	|- (((ph /\ -. ps) -> ch) <-> (ph -> (ps \/ ch)))

Proof of Theorem pm5.6

Step	Hyp	Ref	Expression
1		impexp 347	. 2 |- (((ph /\ -. ps) -> ch) <-> (ph -> (-. ps -> ch)))
2		df-or 224	. . 3 |- ((ps \/ ch) <-> (-. ps -> ch))
3	2	imbi2i 185	. 2 |- ((ph -> (ps \/ ch)) <-> (ph -> (-. ps -> ch)))
4	1, 3	bitr4 176	1 |- (((ph /\ -. ps) -> ch) <-> (ph -> (ps \/ ch)))

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

This theorem is referenced by:  pm5.75 747  ssundif 2334  brdom3 4773

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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