Theorem 3orbi123

Description: pm4.39 with a 3-conjunct antecedent. This proof is 3orbi123VD automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	3orbi123	|- ( ( ( ph <-> ps ) /\ ( ch <-> th ) /\ ( ta <-> et ) ) -> ( ( ph \/ ch \/ ta ) <-> ( ps \/ th \/ et ) ) )

Proof

Step	Hyp	Ref	Expression
1		simp1	|- ( ( ( ph <-> ps ) /\ ( ch <-> th ) /\ ( ta <-> et ) ) -> ( ph <-> ps ) )
2		simp2	|- ( ( ( ph <-> ps ) /\ ( ch <-> th ) /\ ( ta <-> et ) ) -> ( ch <-> th ) )
3		simp3	|- ( ( ( ph <-> ps ) /\ ( ch <-> th ) /\ ( ta <-> et ) ) -> ( ta <-> et ) )
4	1 2 3	3orbi123d	|- ( ( ( ph <-> ps ) /\ ( ch <-> th ) /\ ( ta <-> et ) ) -> ( ( ph \/ ch \/ ta ) <-> ( ps \/ th \/ et ) ) )