exan>

Theorem.

Arguments:

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

Hypotheses:

(x bound in psi)

Assertions:

(existsx(phiwedgepsi)leftrightarrow(existsxphiwedgepsi))

Proof:

Hyp Ref Line Expr
Hypo1(x bound in psi)
df-ex2(existsx(phiwedgepsi)leftrightarrowlnotforallxlnot(phiwedgepsi))
1bv-¬3(x bound in lnotpsi)
3alor>4(forallx(lnotphiveelnotpsi)leftrightarrow(forallxlnotphiveelnotpsi))
nan.or5(lnot(phiwedgepsi)leftrightarrow(lnotphiveelnotpsi))
5eqt-∀-i6(forallxlnot(phiwedgepsi)leftrightarrowforallx(lnotphiveelnotpsi))
nan.or7(lnot(existsxphiwedgepsi)leftrightarrow(lnotexistsxphiveelnotpsi))
aln.ex8(forallxlnotphileftrightarrowlnotexistsxphi)
8bi.bldor<9((forallxlnotphiveelnotpsi)leftrightarrow(lnotexistsxphiveelnotpsi))
7, 9><bitr10(lnot(existsxphiwedgepsi)leftrightarrow(forallxlnotphiveelnotpsi))
4, 6, 10<2bitr11(forallxlnot(phiwedgepsi)leftrightarrowlnot(existsxphiwedgepsi))
11conb>i12((existsxphiwedgepsi)leftrightarrowlnotforallxlnot(phiwedgepsi))
2, 12><bitr13(existsx(phiwedgepsi)leftrightarrow(existsxphiwedgepsi))