eu-sb1

Theorem.

Arguments:

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

Distinct variable conditions:

(x, a),

Assertions:

(([a/x]phiwedgeforallx(phito(xeqa)))to_e1xphi)

Proof:

Hyp Ref Line Expr
siman>1(([a/x]phiwedgeforallx(phito(xeqa)))toforallx(phito(xeqa)))
1mo-sb12(([a/x]phiwedgeforallx(phito(xeqa)))to_em1xphi)
siman<3(([a/x]phiwedgeforallx(phito(xeqa)))to[a/x]phi)
3sb-spec-ex4(([a/x]phiwedgeforallx(phito(xeqa)))toexistsxphi)
2, 4jca5(([a/x]phiwedgeforallx(phito(xeqa)))to(existsxphiwedge_em1xphi))
df-∃1-alt56(_e1xphileftrightarrow(existsxphiwedge_em1xphi))
5, 6brpi22<7(([a/x]phiwedgeforallx(phito(xeqa)))to_e1xphi)