Theorem 3orbi123i

Description: Join 3 biconditionals with disjunction. (Contributed by NM, 17-May-1994)

	Ref	Expression
Hypotheses	bi3.1	|- ( ph <-> ps )
	bi3.2	|- ( ch <-> th )
	bi3.3	|- ( ta <-> et )
Assertion	3orbi123i	|- ( ( ph \/ ch \/ ta ) <-> ( ps \/ th \/ et ) )

Proof

Step	Hyp	Ref	Expression
1		bi3.1	|- ( ph <-> ps )
2		bi3.2	|- ( ch <-> th )
3		bi3.3	|- ( ta <-> et )
4	1 2	orbi12i	|- ( ( ph \/ ch ) <-> ( ps \/ th ) )
5	4 3	orbi12i	|- ( ( ( ph \/ ch ) \/ ta ) <-> ( ( ps \/ th ) \/ et ) )
6		df-3or	|- ( ( ph \/ ch \/ ta ) <-> ( ( ph \/ ch ) \/ ta ) )
7		df-3or	|- ( ( ps \/ th \/ et ) <-> ( ( ps \/ th ) \/ et ) )
8	5 6 7	3bitr4i	|- ( ( ph \/ ch \/ ta ) <-> ( ps \/ th \/ et ) )