imgen>

Theorem.

Arguments:

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

Hypotheses:

(x bound in phi)

Assertions:

(forallx(phitopsi)leftrightarrow(phitoforallxpsi))

Proof:

Hyp Ref Line Expr
Hypo1(x bound in phi)
1df-Bvp2(phitoforallxphi)
al.imdi3(forallx(phitopsi)to(forallxphitoforallxpsi))
2, 3rpi324(forallx(phitopsi)to(phitoforallxpsi))
fv-alx5(forallxpsitoforallxforallxpsi)
2, 5fv-im6((phitoforallxpsi)toforallx(phitoforallxpsi))
ax47(forallxpsitopsi)
7syl<8((phitoforallxpsi)to(phitopsi))
8im.bldal9(forallx(phitoforallxpsi)toforallx(phitopsi))
6, 9syl10((phitoforallxpsi)toforallx(phitopsi))
4, 10>bii11(forallx(phitopsi)leftrightarrow(phitoforallxpsi))