Metamath Proof Explorer


Theorem imbitrdi

Description: A mixed syllogism inference from a nested implication and a biconditional. (Contributed by NM, 21-Jun-1993)

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

Proof

Step Hyp Ref Expression
1 imbitrdi.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 imbitrdi.2 ( 𝜒𝜃 )
3 2 biimpi ( 𝜒𝜃 )
4 1 3 syl6 ( 𝜑 → ( 𝜓𝜃 ) )