Theorem bi3or 607

Description: Join antecedents and consequents with disjunction.

Hypotheses

Ref	Expression
bi3.1	|- (ph <-> ps)
bi3.2	|- (ch <-> th)
bi3.3	|- (ta <-> et)

Assertion

Ref	Expression
bi3or	|- ((ph \/ ch \/ ta ) <-> (ps \/ th \/ et))

Proof of Theorem bi3or

Step	Hyp	Ref	Expression
1		bi3.1	. . . 4 |- (ph <-> ps)
2		bi3.2	. . . 4 |- (ch <-> th)
3	1, 2	orbi12i 216	. . 3 |- ((ph \/ ch) <-> (ps \/ th))
4		bi3.3	. . 3 |- (ta <-> et)
5	3, 4	orbi12i 216	. 2 |- (((ph \/ ch) \/ ta ) <-> ((ps \/ th) \/ et))
6		df-3or 582	. 2 |- ((ph \/ ch \/ ta ) <-> ((ph \/ ch) \/ ta ))
7		df-3or 582	. 2 |- ((ps \/ th \/ et) <-> ((ps \/ th) \/ et))
8	5, 6, 7	3bitr4 158	1 |- ((ph \/ ch \/ ta ) <-> (ps \/ th \/ et))

Syntax hints:   <-> wb 127   \/ wo 195   \/ w3o 580

This theorem is referenced by:  wecmpep 2193  ordon 2238  zorn2 3612

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197  df-3or 582

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