bexim

Theorem.

Arguments:

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

Assertions:

(existsx(phitopsi)leftrightarrow(forallxphitoexistsxpsi))

Proof:

Hyp Ref Line Expr
al.andi1(forallx(phiwedgelnotpsi)leftrightarrow(forallxphiwedgeforallxlnotpsi))
an.nim2((phiwedgelnotpsi)leftrightarrowlnot(phitopsi))
2eqt-∀-i3(forallx(phiwedgelnotpsi)leftrightarrowforallxlnot(phitopsi))
df-an4((forallxphiwedgeforallxlnotpsi)leftrightarrowlnot(forallxphitolnotforallxlnotpsi))
1, 3, 4>2bitr5(forallxlnot(phitopsi)leftrightarrowlnot(forallxphitolnotforallxlnotpsi))
5conb>i6((forallxphitolnotforallxlnotpsi)leftrightarrowlnotforallxlnot(phitopsi))
df-ex7(existsxpsileftrightarrowlnotforallxlnotpsi)
7bi.bldim>8((forallxphitoexistsxpsi)leftrightarrow(forallxphitolnotforallxlnotpsi))
df-ex9(existsx(phitopsi)leftrightarrowlnotforallxlnot(phitopsi))
6, 8, 9<2bitr<10(existsx(phitopsi)leftrightarrow(forallxphitoexistsxpsi))