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Metamath Proof Explorer

Theorem 3bitr3ri

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypotheses 3bitr3i.1 
|- ( ph <-> ps )
3bitr3i.2 
|- ( ph <-> ch )
3bitr3i.3 
|- ( ps <-> th )
Assertion 3bitr3ri 
|- ( th <-> ch )

Proof

Step Hyp Ref Expression
1 3bitr3i.1 
 |-  ( ph <-> ps )
2 3bitr3i.2 
 |-  ( ph <-> ch )
3 3bitr3i.3 
 |-  ( ps <-> th )
4 1 2 bitr3i 
 |-  ( ps <-> ch )
5 3 4 bitr3i 
 |-  ( th <-> ch )