aaan

Theorem.

Arguments:

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

Hypotheses:

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

Assertions:

(forallxforally(phiwedgepsi)leftrightarrow(forallxphiwedgeforallypsi))

Proof:

Hyp Ref Line Expr
Hypo1(x bound in psi)
2(y bound in phi)
2alan<3(forally(phiwedgepsi)leftrightarrow(phiwedgeforallypsi))
3eqt-∀-i4(forallxforally(phiwedgepsi)leftrightarrowforallx(phiwedgeforallypsi))
1bv-∀5(x bound in forallypsi)
5alan>6(forallx(phiwedgeforallypsi)leftrightarrow(forallxphiwedgeforallypsi))
4, 6bitr7(forallxforally(phiwedgepsi)leftrightarrow(forallxphiwedgeforallypsi))