Metamath Proof Explorer


Theorem bitrdi

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

Ref Expression
Hypotheses bitrdi.1 ( 𝜑 → ( 𝜓𝜒 ) )
bitrdi.2 ( 𝜒𝜃 )
Assertion bitrdi ( 𝜑 → ( 𝜓𝜃 ) )

Proof

Step Hyp Ref Expression
1 bitrdi.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 bitrdi.2 ( 𝜒𝜃 )
3 2 a1i ( 𝜑 → ( 𝜒𝜃 ) )
4 1 3 bitrd ( 𝜑 → ( 𝜓𝜃 ) )