Theorem pm5.53 483

Description: Theorem *5.53 of [WhiteheadRussell] p. 125.

Assertion

Ref	Expression
pm5.53	|- ((((ph \/ ps) \/ ch) -> th) <-> (((ph -> th) /\ (ps -> th)) /\ (ch -> th)))

Proof of Theorem pm5.53

Step	Hyp	Ref	Expression
1		jaob 422	. 2 |- ((((ph \/ ps) \/ ch) -> th) <-> (((ph \/ ps) -> th) /\ (ch -> th)))
2		jaob 422	. . 3 |- (((ph \/ ps) -> th) <-> ((ph -> th) /\ (ps -> th)))
3	2	anbi1i 481	. 2 |- ((((ph \/ ps) -> th) /\ (ch -> th)) <-> (((ph -> th) /\ (ps -> th)) /\ (ch -> th)))
4	1, 3	bitr 173	1 |- ((((ph \/ ps) \/ ch) -> th) <-> (((ph -> th) /\ (ps -> th)) /\ (ch -> th)))

Syntax hints:   -> 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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