let A be QC-alphabet ; :: thesis: for x being bound_QC-variable of A
for p being Element of QC-WFF A st p is atomic holds
p . x = (the_pred_symbol_of p) ! (Subst ((the_arguments_of p),((A a. 0) .--> x)))
let x be bound_QC-variable of A; :: thesis: for p being Element of QC-WFF A st p is atomic holds
p . x = (the_pred_symbol_of p) ! (Subst ((the_arguments_of p),((A a. 0) .--> x)))
let p be Element of QC-WFF A; :: thesis: ( p is atomic implies p . x = (the_pred_symbol_of p) ! (Subst ((the_arguments_of p),((A a. 0) .--> x))) )
ex F being Function of (QC-WFF A),(QC-WFF A) st
( p . x = F . p & ( for q being Element of QC-WFF A holds
( F . (VERUM A) = VERUM A & ( q is atomic implies F . q = (the_pred_symbol_of q) ! (Subst ((the_arguments_of q),((A a. 0) .--> x))) ) & ( q is negative implies F . q = 'not' (F . (the_argument_of q)) ) & ( q is conjunctive implies F . q = (F . (the_left_argument_of q)) '&' (F . (the_right_argument_of q)) ) & ( q is universal implies F . q = IFEQ ((bound_in q),x,q,(All ((bound_in q),(F . (the_scope_of q))))) ) ) ) ) by Def3;
hence ( p is atomic implies p . x = (the_pred_symbol_of p) ! (Subst ((the_arguments_of p),((A a. 0) .--> x))) ) ; :: thesis: verum