bv-sbb-dv

Theorem.

Arguments:

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

Dummy variables:

z (sv),

Distinct variable conditions:

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

Assertions:

(x bound in [y/x]phi)

Proof:

Hyp Ref Line Expr
bv-∃b1(x bound in existsx((xeqz)wedgephi))
ax17-bv2(x bound in (zeqy))
1, 2bv-∧3(x bound in ((zeqy)wedgeexistsx((xeqz)wedgephi)))
3bv-∃4(x bound in existsz((zeqy)wedgeexistsx((xeqz)wedgephi)))
df-sb5([y/x]phileftrightarrowexistsz((zeqy)wedgeexistsx((xeqz)wedgephi)))
4, 5bvdef6(x bound in [y/x]phi)