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 ψ χ
imbitrdi.2 χ θ
Assertion imbitrdi φ ψ θ

Proof

Step Hyp Ref Expression
1 imbitrdi.1 φ ψ χ
2 imbitrdi.2 χ θ
3 2 biimpi χ θ
4 1 3 syl6 φ ψ θ