Metamath Proof Explorer


Theorem bitr4di

Description: A syllogism inference from two biconditionals. (Contributed by NM, 12-Mar-1993)

Ref Expression
Hypotheses bitr4di.1 ( 𝜑 → ( 𝜓𝜒 ) )
bitr4di.2 ( 𝜃𝜒 )
Assertion bitr4di ( 𝜑 → ( 𝜓𝜃 ) )

Proof

Step Hyp Ref Expression
1 bitr4di.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 bitr4di.2 ( 𝜃𝜒 )
3 2 bicomi ( 𝜒𝜃 )
4 1 3 bitrdi ( 𝜑 → ( 𝜓𝜃 ) )