Metamath Proof Explorer


Theorem 3bitr2ri

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006)

Ref Expression
Hypotheses 3bitr2i.1
|- ( ph <-> ps )
3bitr2i.2
|- ( ch <-> ps )
3bitr2i.3
|- ( ch <-> th )
Assertion 3bitr2ri
|- ( th <-> ph )

Proof

Step Hyp Ref Expression
1 3bitr2i.1
 |-  ( ph <-> ps )
2 3bitr2i.2
 |-  ( ch <-> ps )
3 3bitr2i.3
 |-  ( ch <-> th )
4 1 2 bitr4i
 |-  ( ph <-> ch )
5 4 3 bitr2i
 |-  ( th <-> ph )