alexor-pre

Theorem.

Arguments:

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

Assertions:

(forallx(phiveepsi)to(forallxphiveeexistsxpsi))

Proof:

Hyp Ref Line Expr
al.imdi1(forallx(lnotpsitophi)to(forallxlnotpsitoforallxphi))
orcom2((phiveepsi)leftrightarrow(psiveephi))
df-or3((psiveephi)leftrightarrow(lnotpsitophi))
2, 3bitr4((phiveepsi)leftrightarrow(lnotpsitophi))
4eqt-∀-i5(forallx(phiveepsi)leftrightarrowforallx(lnotpsitophi))
orcom6((forallxphiveelnotforallxlnotpsi)leftrightarrow(lnotforallxlnotpsiveeforallxphi))
df-ex7(existsxpsileftrightarrowlnotforallxlnotpsi)
7bi.bldor>8((forallxphiveeexistsxpsi)leftrightarrow(forallxphiveelnotforallxlnotpsi))
im.or9((forallxlnotpsitoforallxphi)leftrightarrow(lnotforallxlnotpsiveeforallxphi))
6, 8, 9<2bitr10((forallxphiveeexistsxpsi)leftrightarrow(forallxlnotpsitoforallxphi))
1, 5, 10<imtr11(forallx(phiveepsi)to(forallxphiveeexistsxpsi))