Let \$$a,b \in P\$$ and subset \$$A = \\{ a \leq b \; and \; b \leq a \\}\$$. Then you get two meets namely, \$$a \wedge b = a\$$ and \$$b \wedge a = b\$$?

Using reflexivity and transitivity, we can expand this out into a transitivity triangle and get 1. \$$a \leq b \leq a\$$ and \$$a \leq a\$$ and 2. \$$b \leq a \leq b\$$ and \$$b \leq b\$$. Taking \$$a \wedge b\$$ in Triangle 1 and Triangle 2 gives a and b respectively.