mo-sb1

Theorem.

Arguments:

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

Dummy variables:

z (sv),

Distinct variable conditions:

(z, a), (z, x), (z, phi), (x, a),

Assertions:

(forallx(phito(xeqa))to_em1xphi)

Proof:

Hyp Ref Line Expr
eqt>1((zeqa)to((xeqz)leftrightarrow(xeqa)))
1bi.bldim>d2((zeqa)to((phito(xeqz))leftrightarrow(phito(xeqa))))
2bi.bldald3((zeqa)to(forallx(phito(xeqz))leftrightarrowforallx(phito(xeqa))))
ax17-bv4(z bound in forallx(phito(xeqa)))
3, 4sb-xplw5(forallx(phito(xeqa))to[a/z]forallx(phito(xeqz)))
5sb-spec-ex6(forallx(phito(xeqa))toexistszforallx(phito(xeqz)))
df-∃mo-alt27(existszforallx(phito(xeqz))to_em1xphi)
6, 7syl8(forallx(phito(xeqa))to_em1xphi)