let s be natural Number ; :: thesis: ( s >= 1 implies s choose 1 = s )
A0: s is Nat by TARSKI:1;
defpred S₁[ Nat] means $1 choose 1 = $1;

A1: now :: thesis: for n being Nat st n >= 1 & S₁[n] holds
S₁[n + 1]

let n be Nat; :: thesis: ( n >= 1 & S₁[n] implies S₁[n + 1] )
assume that
n >= 1 and
A2: S₁[n] ; :: thesis: S₁[n + 1]
(n + 1) choose 1 = (n + 1) choose (0 + 1)
.= n + (n choose 0) by A2, Th22
.= n + 1 by Th19 ;
hence S₁[n + 1] ; :: thesis: verum

end;

A3: S₁[1] by Th21;
for n being Nat st n >= 1 holds
S₁[n] from NAT_1:sch 8(A3, A1);
hence ( s >= 1 implies s choose 1 = s ) by A0; :: thesis: verum