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 ψ χ
imbitrrdi.2 θ χ
Assertion imbitrrdi φ ψ θ

Proof

Step Hyp Ref Expression
1 imbitrrdi.1 φ ψ χ
2 imbitrrdi.2 θ χ
3 2 biimpri χ θ
4 1 3 syl6 φ ψ θ