assume
not MP-conectives misses MP-variables
; contradiction
then consider x being object such that
A1:
x in [:{0,1,2},NAT:]
and
A2:
x in [:{3},NAT:]
by XBOOLE_0:3;
consider x1, x2 being object such that
A3:
x1 in {0,1,2}
and
x2 in NAT
and
A4:
x = [x1,x2]
by A1, ZFMISC_1:def 2;
x1 = 3
by A2, A4, ZFMISC_1:105;
hence
contradiction
by A3, ENUMSET1:def 1; verum