This paper presents a direct proof of the BCF recursion relation for tree-level Yang-Mills amplitudes. The recursion relation expresses a tree-level amplitude as a sum over terms constructed from the product of two subamplitudes with fewer gluons and a Feynman propagator. The proof uses properties of tree-level amplitudes only, without relying on one-loop amplitudes. The key idea is to consider a function A(z) that depends on a complex parameter z, and to show that it has only simple poles. By analyzing the residues of these poles, the recursion relation is derived. The proof also shows that the amplitude vanishes at infinity for certain helicity configurations, which is essential for the recursion relation to hold. The paper also demonstrates that MHV tree diagrams give the same Yang-Mills tree amplitudes as Feynman diagrams. The BCF recursion relations are shown to be equivalent to the MHV recursion relations, and they provide a convenient way to compute tree-level amplitudes from their singularities. The paper concludes by showing that the MHV tree diagrams generate the same singularities as Feynman diagrams, and that the equality of the two amplitudes follows from the analysis of singularities and Lorentz invariance.This paper presents a direct proof of the BCF recursion relation for tree-level Yang-Mills amplitudes. The recursion relation expresses a tree-level amplitude as a sum over terms constructed from the product of two subamplitudes with fewer gluons and a Feynman propagator. The proof uses properties of tree-level amplitudes only, without relying on one-loop amplitudes. The key idea is to consider a function A(z) that depends on a complex parameter z, and to show that it has only simple poles. By analyzing the residues of these poles, the recursion relation is derived. The proof also shows that the amplitude vanishes at infinity for certain helicity configurations, which is essential for the recursion relation to hold. The paper also demonstrates that MHV tree diagrams give the same Yang-Mills tree amplitudes as Feynman diagrams. The BCF recursion relations are shown to be equivalent to the MHV recursion relations, and they provide a convenient way to compute tree-level amplitudes from their singularities. The paper concludes by showing that the MHV tree diagrams generate the same singularities as Feynman diagrams, and that the equality of the two amplitudes follows from the analysis of singularities and Lorentz invariance.