alexan>

Theorem.

Arguments:

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

Assertions:

((forallxphiwedgeexistsxpsi)toexistsx(phiwedgepsi))

Proof:

Hyp Ref Line Expr
al.imdi1(forallx(phitolnotpsi)to(forallxphitoforallxlnotpsi))
aln.ex2(forallxlnotpsileftrightarrowlnotexistsxpsi)
1, 2brpi333(forallx(phitolnotpsi)to(forallxphitolnotexistsxpsi))
3con4(lnot(forallxphitolnotexistsxpsi)tolnotforallx(phitolnotpsi))
df-an5((forallxphiwedgeexistsxpsi)leftrightarrowlnot(forallxphitolnotexistsxpsi))
exn.al6(existsxlnot(phitolnotpsi)leftrightarrowlnotforallx(phitolnotpsi))
4, 5, 6<imtr7((forallxphiwedgeexistsxpsi)toexistsxlnot(phitolnotpsi))
df-an8((phiwedgepsi)leftrightarrowlnot(phitolnotpsi))
8eqt-∃-i9(existsx(phiwedgepsi)leftrightarrowexistsxlnot(phitolnotpsi))
7, 9brpi22<10((forallxphiwedgeexistsxpsi)toexistsx(phiwedgepsi))