chvar-∀-w

Theorem.

Arguments:

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

Distinct variable conditions:

(y, x),

Hypotheses:

(y bound in phi)

Assertions:

(forally[y/x]phileftrightarrowforallxphi)

Proof:

Hyp Ref Line Expr
Hypo1(y bound in phi)
chvar-∀-1w2(forally[y/x]phileftrightarrowforallx[x/y]phi)
1sb-bv3([x/y]phileftrightarrowphi)
3eqt-∀-i4(forallx[x/y]phileftrightarrowforallxphi)
2, 4bitr5(forally[y/x]phileftrightarrowforallxphi)