Metamath Proof Explorer

Theorem 3imtr4i

Description: A mixed syllogism inference, useful for applying a definition to both sides of an implication. (Contributed by NM, 3-Jan-1993)

Ref Expression
Hypotheses 3imtr4.1 φ ψ
3imtr4.2 χ φ
3imtr4.3 θ ψ
Assertion 3imtr4i χ θ


Step Hyp Ref Expression
1 3imtr4.1 φ ψ
2 3imtr4.2 χ φ
3 3imtr4.3 θ ψ
4 2 1 sylbi χ ψ
5 4 3 sylibr χ θ