consider F being Function of (QC-WFF F₁()),F₂() such that
A3: F₉(F₄()) = F . F₄() and
A4: for p being Element of QC-WFF F₁()
for d1, d2 being Element of F₂() holds
( ( p = VERUM F₁() implies F . p = F₃() ) & ( p is atomic implies F . p = F₅(p) ) & ( p is negative & d1 = F . (the_argument_of p) implies F . p = F₆(d1) ) & ( p is conjunctive & d1 = F . (the_left_argument_of p) & d2 = F . (the_right_argument_of p) implies F . p = F₇(d1,d2) ) & ( p is universal & d1 = F . (the_scope_of p) implies F . p = F₈(p,d1) ) ) by A1;
F . (the_scope_of F₄()) = F₉((the_scope_of F₄())) by A1, A4;
hence F₉(F₄()) = F₈(F₄(),F₉((the_scope_of F₄()))) by A2, A3, A4; :: thesis: verum