let x be bound_QC-variable; :: thesis: for p being Element of QC-WFF
for V being non empty Subset of QC-variables holds Vars ((All (x,p)),V) = Vars (p,V)
let p be Element of QC-WFF ; :: thesis: for V being non empty Subset of QC-variables holds Vars ((All (x,p)),V) = Vars (p,V)
let V be non empty Subset of QC-variables; :: thesis: Vars ((All (x,p)),V) = Vars (p,V)
A1: All (x,p) is universal by QC_LANG1:def 20;
then the_scope_of (All (x,p)) = p by QC_LANG1:def 27;
hence Vars ((All (x,p)),V) = Vars (p,V) by A1, Lm2; :: thesis: verum