Metamath Proof Explorer


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 ) ) )