import tactic.

variables a b c d e : Bool.
axiom H1 : a => b.
axiom H2 : b = c.
axiom H3 : c => d.
axiom H4 : d <=> e.

theorem T : a => e
:= calc a  =>  b : H1
      ...  =   c : H2
      ...  =>  d : (by apply H3)
      ...  <=> e : H4.