let x be bound_QC-variable; :: thesis: for p, q being Element of QC-WFF holds (p '&' q) . x = (p . x) '&' (q . x)
let p, q be Element of QC-WFF ; :: thesis: (p '&' q) . x = (p . x) '&' (q . x)
set pq = p '&' q;
A1: p '&' q is conjunctive by QC_LANG1:def 18;
then ( the_left_argument_of (p '&' q) = p & the_right_argument_of (p '&' q) = q ) by QC_LANG1:def 23, QC_LANG1:def 24;
hence (p '&' q) . x = (p . x) '&' (q . x) by A1, Th33; :: thesis: verum