Theorem 3orbi123i 823

Description: Join 3 biconditionals with disjunction.

Hypotheses

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

Assertion

Ref	Expression
3orbi123i	|- ((ph \/ ch \/ ta) <-> (ps \/ th \/ et))

Proof of Theorem 3orbi123i

Step	Hyp	Ref	Expression
1		bi3.1	. . . 4 |- (ph <-> ps)
2		bi3.2	. . . 4 |- (ch <-> th)
3	1, 2	orbi12i 257	. . 3 |- ((ph \/ ch) <-> (ps \/ th))
4		bi3.3	. . 3 |- (ta <-> et)
5	3, 4	orbi12i 257	. 2 |- (((ph \/ ch) \/ ta) <-> ((ps \/ th) \/ et))
6		df-3or 776	. 2 |- ((ph \/ ch \/ ta) <-> ((ph \/ ch) \/ ta))
7		df-3or 776	. 2 |- ((ps \/ th \/ et) <-> ((ps \/ th) \/ et))
8	5, 6, 7	3bitr4 183	1 |- ((ph \/ ch \/ ta) <-> (ps \/ th \/ et))

Syntax hints:   <-> wb 146   \/ wo 222   \/ w3o 774

This theorem is referenced by:  wecmpep 2941  ordon 2987  cnvso 3523  zorn 4797

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-3or 776

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