bv-∃1b

Theorem.

Arguments:

x (sv), phi (pr),

Dummy variables:

y (sv),

Distinct variable conditions:

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

Assertions:

(x bound in _e1xphi)

Proof:

Hyp Ref Line Expr
bv-∀b1(x bound in forallx(phileftrightarrow(xeqy)))
1bv-∃2(x bound in existsyforallx(phileftrightarrow(xeqy)))
2df-Bvp3(existsyforallx(phileftrightarrow(xeqy))toforallxexistsyforallx(phileftrightarrow(xeqy)))
df-∃14(_e1xphileftrightarrowexistsyforallx(phileftrightarrow(xeqy)))
4eqt-∀-i5(forallx_e1xphileftrightarrowforallxexistsyforallx(phileftrightarrow(xeqy)))
3, 4, 5<imtr6(_e1xphitoforallx_e1xphi)
6df-Bvp7(x bound in _e1xphi)