Theorem pm5.53 771

Description: Theorem *5.53 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

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 758	. 2 |- ((((ph \/ ps) \/ ch) -> th) <-> (((ph \/ ps) -> th) /\ (ch -> th)))
2		jaob 758	. . 3 |- (((ph \/ ps) -> th) <-> ((ph -> th) /\ (ps -> th)))
3	2	anbi1i 676	. 2 |- ((((ph \/ ps) -> th) /\ (ch -> th)) <-> (((ph -> th) /\ (ps -> th)) /\ (ch -> th)))
4	1, 3	bitri 240	1 |- ((((ph \/ ps) \/ ch) -> th) <-> (((ph -> th) /\ (ps -> th)) /\ (ch -> th)))

Syntax hints:   -> wi 4   <-> wb 176   \/ wo 357   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by: (None)