ex.ordi

Theorem.

Arguments:

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

Assertions:

(existsx(phiveepsi)leftrightarrow(existsxphiveeexistsxpsi))

Proof:

Hyp Ref Line Expr
nor.an1(lnot(phiveepsi)leftrightarrow(lnotphiwedgelnotpsi))
1eqt-∀-i2(forallxlnot(phiveepsi)leftrightarrowforallx(lnotphiwedgelnotpsi))
al.andi3(forallx(lnotphiwedgelnotpsi)leftrightarrow(forallxlnotphiwedgeforallxlnotpsi))
aln.ex4(forallxlnotphileftrightarrowlnotexistsxphi)
aln.ex5(forallxlnotpsileftrightarrowlnotexistsxpsi)
4, 5bi.bldan<>6((forallxlnotphiwedgeforallxlnotpsi)leftrightarrow(lnotexistsxphiwedgelnotexistsxpsi))
2, 3, 62bitr7(forallxlnot(phiveepsi)leftrightarrow(lnotexistsxphiwedgelnotexistsxpsi))
7bi.bldneg8(lnotforallxlnot(phiveepsi)leftrightarrowlnot(lnotexistsxphiwedgelnotexistsxpsi))
df-ex9(existsx(phiveepsi)leftrightarrowlnotforallxlnot(phiveepsi))
or.an10((existsxphiveeexistsxpsi)leftrightarrowlnot(lnotexistsxphiwedgelnotexistsxpsi))
8, 9, 10<2bitr11(existsx(phiveepsi)leftrightarrow(existsxphiveeexistsxpsi))