fv.eqex

Theorem.

Arguments:

x (sv), phi (pr),

Hypotheses:

(x bound in phi)

Assertions:

(phileftrightarrowexistsxphi)

Proof:

Hyp Ref Line Expr
Hypo1(x bound in phi)
1df-Bvp2(phitoforallxphi)
spec-ex3(phitoexistsxphi)
df-ex4(existsxphileftrightarrowlnotforallxlnotphi)
2con5(lnotforallxphitolnotphi)
5im.bldal6(forallxlnotforallxphitoforallxlnotphi)
6con7(lnotforallxlnotphitolnotforallxlnotforallxphi)
ax68(lnotforallxlnotforallxphitophi)
7, 8syl9(lnotforallxlnotphitophi)
4, 9brpi2110(existsxphitophi)
3, 10>bii11(phileftrightarrowexistsxphi)