Theorem 3or6 1263

Description: Analog of or4 514 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.)

Assertion

Ref	Expression
3or6	|- (((ph \/ ps) \/ (ch \/ th) \/ (ta \/ et)) <-> ((ph \/ ch \/ ta) \/ (ps \/ th \/ et)))

Proof of Theorem 3or6

Step	Hyp	Ref	Expression
1		or4 514	. . 3 |- ((((ph \/ ch) \/ ta) \/ ((ps \/ th) \/ et)) <-> (((ph \/ ch) \/ (ps \/ th)) \/ (ta \/ et)))
2		or4 514	. . . 4 |- (((ph \/ ch) \/ (ps \/ th)) <-> ((ph \/ ps) \/ (ch \/ th)))
3	2	orbi1i 506	. . 3 |- ((((ph \/ ch) \/ (ps \/ th)) \/ (ta \/ et)) <-> (((ph \/ ps) \/ (ch \/ th)) \/ (ta \/ et)))
4	1, 3	bitr2i 241	. 2 |- ((((ph \/ ps) \/ (ch \/ th)) \/ (ta \/ et)) <-> (((ph \/ ch) \/ ta) \/ ((ps \/ th) \/ et)))
5		df-3or 935	. 2 |- (((ph \/ ps) \/ (ch \/ th) \/ (ta \/ et)) <-> (((ph \/ ps) \/ (ch \/ th)) \/ (ta \/ et)))
6		df-3or 935	. . 3 |- ((ph \/ ch \/ ta) <-> ((ph \/ ch) \/ ta))
7		df-3or 935	. . 3 |- ((ps \/ th \/ et) <-> ((ps \/ th) \/ et))
8	6, 7	orbi12i 507	. 2 |- (((ph \/ ch \/ ta) \/ (ps \/ th \/ et)) <-> (((ph \/ ch) \/ ta) \/ ((ps \/ th) \/ et)))
9	4, 5, 8	3bitr4i 268	1 |- (((ph \/ ps) \/ (ch \/ th) \/ (ta \/ et)) <-> ((ph \/ ch \/ ta) \/ (ps \/ th \/ et)))

Syntax hints:   <-> wb 176   \/ wo 357   \/ w3o 933

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-3or 935

This theorem is referenced by: (None)