dfsb-alt

Theorem.

Arguments:

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

Distinct variable conditions:

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

Hypotheses:

(z bound in phi)

Assertions:

([y/x]phileftrightarrowexistsz((zeqy)wedgeforallx((xeqz)tophi)))

Proof:

Hyp Ref Line Expr
Hypo1(z bound in phi)
1sbco2w2([y/z][z/x]phileftrightarrow[y/x]phi)
2bicomi3([y/x]phileftrightarrow[y/z][z/x]phi)
dfsb-dval4([z/x]phileftrightarrowforallx((xeqz)tophi))
dfsb-dvex5([y/z][z/x]phileftrightarrowexistsz((zeqy)wedge[z/x]phi))
4bi.bldan>6(((zeqy)wedge[z/x]phi)leftrightarrow((zeqy)wedgeforallx((xeqz)tophi)))
6eqt-∃-i7(existsz((zeqy)wedge[z/x]phi)leftrightarrowexistsz((zeqy)wedgeforallx((xeqz)tophi)))
3, 5, 72bitr8([y/x]phileftrightarrowexistsz((zeqy)wedgeforallx((xeqz)tophi)))