cbvexd

Theorem.

Arguments:

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

Distinct variable conditions:

(x, phi), (x, chi),

Hypotheses:

(phito((xeqy)to(psileftrightarrowchi)))
(phito(psitoforallypsi))
(y bound in phi)

Assertions:

(phito(existsxpsileftrightarrowexistsychi))

Proof:

Hyp Ref Line Expr
Hypo1(phito((xeqy)to(psileftrightarrowchi)))
2(phito(psitoforallypsi))
3(y bound in phi)
2, 3fv-negd4(phito(lnotpsitoforallylnotpsi))
conb5((psileftrightarrowchi)leftrightarrow(lnotpsileftrightarrowlnotchi))
1, 5brpi336(phito((xeqy)to(lnotpsileftrightarrowlnotchi)))
3, 4, 6cbvald7(phito(forallxlnotpsileftrightarrowforallylnotchi))
7bi.bldnegd8(phito(lnotforallxlnotpsileftrightarrowlnotforallylnotchi))
df-ex9(existsxpsileftrightarrowlnotforallxlnotpsi)
df-ex10(existsychileftrightarrowlnotforallylnotchi)
8, 9, 10<2bitrg11(phito(existsxpsileftrightarrowexistsychi))