so it is a reflection like if we say(β+1) is a "transformation factor", any resistance at the base is seen (reflect it to the emitter) at the emitter as a β + 1 smaller resistance ( re = r_pi/(β + 1 ) ).
And any resistance at the emitter is seen at the base node as a (β + 1) large resistance r_pi = ( β + 1)*re
vre = re * ie is the same of vre = βre * ib and it depends just upon the node we're looking at the circuit from right ?