ax10ex

Theorem.

Arguments:

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

Assertions:

(forallx(xeqy)to(existsxphileftrightarrowexistsyphi))

Proof:

Hyp Ref Line Expr
ax10b1(forallx(xeqy)to(forallxlnotphileftrightarrowforallylnotphi))
aln.ex2(forallxlnotphileftrightarrowlnotexistsxphi)
aln.ex3(forallylnotphileftrightarrowlnotexistsyphi)
1, 2, 3>2bitrg4(forallx(xeqy)to(lnotexistsxphileftrightarrowlnotexistsyphi))
4bi.bldnegd5(forallx(xeqy)to(lnotlnotexistsxphileftrightarrowlnotlnotexistsyphi))
bneg>6(existsxphileftrightarrowlnotlnotexistsxphi)
bneg>7(existsyphileftrightarrowlnotlnotexistsyphi)
5, 6, 7<2bitrg8(forallx(xeqy)to(existsxphileftrightarrowexistsyphi))