let IT1, IT2 be Nat; :: thesis: ( phi is IT1 -wff & ( for n being Nat st phi is n -wff holds
IT1 <= n ) & phi is IT2 -wff & ( for n being Nat st phi is n -wff holds
IT2 <= n ) implies IT1 = IT2 )
assume B1: ( phi is IT1 -wff & ( for n being Nat st phi is n -wff holds
IT1 <= n ) ) ; :: thesis: ( not phi is IT2 -wff or ex n being Nat st
( phi is n -wff & not IT2 <= n ) or IT1 = IT2 )
assume B2: ( phi is IT2 -wff & ( for n being Nat st phi is n -wff holds
IT2 <= n ) ) ; :: thesis: IT1 = IT2
B3: IT2 <= IT1 by B2, B1;
IT1 <= IT2 by B1, B2;
hence IT1 = IT2 by B3, XXREAL_0:1; :: thesis: verum