imgen2>

Theorem.

Arguments:

x (sv), y (sv), phi (pr), psi (pr),

Hypotheses:

(y bound in phi)
(x bound in phi)

Assertions:

(forallxforally(phitopsi)leftrightarrow(phitoforallxforallypsi))

Proof:

Hyp Ref Line Expr
Hypo1(y bound in phi)
2(x bound in phi)
1imgen>3(forally(phitopsi)leftrightarrow(phitoforallypsi))
3eqt-∀-i4(forallxforally(phitopsi)leftrightarrowforallx(phitoforallypsi))
2imgen>5(forallx(phitoforallypsi)leftrightarrow(phitoforallxforallypsi))
4, 5bitr6(forallxforally(phitopsi)leftrightarrow(phitoforallxforallypsi))