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Metamath Proof Explorer

Theorem 3bitr2i

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 3bitr2i 
|- ( ph <-> th )

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 bitri 
 |-  ( ph <-> th )