Metamath Proof Explorer


Theorem imbitrrdi

Description: A mixed syllogism inference from a nested implication and a biconditional. Useful for substituting an embedded consequent with a definition. (Contributed by NM, 5-Aug-1993)

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

Proof

Step Hyp Ref Expression
1 imbitrrdi.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 imbitrrdi.2 ( 𝜃𝜒 )
3 2 biimpri ( 𝜒𝜃 )
4 1 3 syl6 ( 𝜑 → ( 𝜓𝜃 ) )