let y be Element of X2; :: thesis: ( y = x `2_3 iff for x1, x2, x3 being object st x = [x1,x2,x3] holds
y = x2 )
thus ( y = x `2_3 implies for x1, x2, x3 being object st x = [x1,x2,x3] holds
y = x2 ) ; :: thesis: ( ( for x1, x2, x3 being object st x = [x1,x2,x3] holds
y = x2 ) implies y = x `2_3 )
assume A5: for x1, x2, x3 being object st x = [x1,x2,x3] holds
y = x2 ; :: thesis: y = x `2_3
consider xx1 being Element of X1, xx2 being Element of X2, xx3 being Element of X3 such that
A6: x = [xx1,xx2,xx3] by Lm2;
thus y = x `2_3 by A5, A6; :: thesis: verum