eqt-∃1-d

Theorem.

Arguments:

x (sv), phi (pr), psi (pr), chi (pr),

Dummy variables:

y (sv),

Distinct variable conditions:

(y, x), (y, phi), (y, psi), (y, chi),

Hypotheses:

(phito(psileftrightarrowchi))
(x bound in phi)

Assertions:

(phito(_e1xpsileftrightarrow_e1xchi))

Proof:

Hyp Ref Line Expr
Hypo1(phito(psileftrightarrowchi))
2(x bound in phi)
1bi.bldbi<d3(phito((psileftrightarrow(xeqy))leftrightarrow(chileftrightarrow(xeqy))))
2, 3bi.bldald4(phito(forallx(psileftrightarrow(xeqy))leftrightarrowforallx(chileftrightarrow(xeqy))))
4bi.bldexd5(phito(existsyforallx(psileftrightarrow(xeqy))leftrightarrowexistsyforallx(chileftrightarrow(xeqy))))
df-∃16(_e1xpsileftrightarrowexistsyforallx(psileftrightarrow(xeqy)))
df-∃17(_e1xchileftrightarrowexistsyforallx(chileftrightarrow(xeqy)))
5, 6, 7<2bitrg8(phito(_e1xpsileftrightarrow_e1xchi))