@user21820

A: prove that any non-trivial tree actually has at least two vertices of degree one.
B: prove that every simple graph with at least two vertices has two vertices of the same degree

Does proving B first immediately make A trivial in the fact that we could classify a non-trivial tree as a simple graph, and by substitution, A is true?

How I need to show that this conclusion is true?
Check the validity of the following argument:
(1) If I try and I have talent then I can be a Mathematician.
(2) If I become a Mathematician, then I will be happy.
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Therefore, if I will not be happy, then I did not try hard or I do not have talent.