cbvex

Theorem.

Arguments:

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

Hypotheses:

((xeqy)to(phileftrightarrowpsi))
(x bound in psi)
(y bound in phi)

Assertions:

(existsxphileftrightarrowexistsypsi)

Proof:

Hyp Ref Line Expr
Hypo1((xeqy)to(phileftrightarrowpsi))
2(x bound in psi)
3(y bound in phi)
3bv-¬4(y bound in lnotphi)
2bv-¬5(x bound in lnotpsi)
1bi.bldnegd6((xeqy)to(lnotphileftrightarrowlnotpsi))
4, 5, 6cbval7(forallxlnotphileftrightarrowforallylnotpsi)
7bi.bldneg8(lnotforallxlnotphileftrightarrowlnotforallylnotpsi)
df-ex9(existsxphileftrightarrowlnotforallxlnotphi)
df-ex10(existsypsileftrightarrowlnotforallylnotpsi)
8, 9, 10<2bitr11(existsxphileftrightarrowexistsypsi)