chvar-∀

Theorem.

Arguments:

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

Dummy variables:

z (sv),

Distinct variable conditions:

(z, y), (z, x), (z, phi),

Hypotheses:

(y bound in phi)

Assertions:

(forally[y/x]phileftrightarrowforallxphi)

Proof:

Hyp Ref Line Expr
Hypo1(y bound in phi)
ax17-bv2(z bound in phi)
1bv-sb-d13(y bound in [z/x]phi)
2chvar-∀-w4(forallz[z/x]phileftrightarrowforallxphi)
3chvar-∀-w5(forally[y/z][z/x]phileftrightarrowforallz[z/x]phi)
4, 5bitr6(forally[y/z][z/x]phileftrightarrowforallxphi)
2sbco2w7([y/z][z/x]phileftrightarrow[y/x]phi)
7eqt-∀-i8(forally[y/z][z/x]phileftrightarrowforally[y/x]phi)
6, 8<>bitr9(forally[y/x]phileftrightarrowforallxphi)