Metamath Proof Explorer


Theorem biimtrrid

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

Ref Expression
Hypotheses biimtrrid.1 ψ φ
biimtrrid.2 χ ψ θ
Assertion biimtrrid χ φ θ

Proof

Step Hyp Ref Expression
1 biimtrrid.1 ψ φ
2 biimtrrid.2 χ ψ θ
3 1 biimpri φ ψ
4 3 2 syl5 χ φ θ