alor<

Theorem.

Arguments:

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

Hypotheses:

(x bound in phi)

Assertions:

(forallx(phiveepsi)leftrightarrow(phiveeforallxpsi))

Proof:

Hyp Ref Line Expr
Hypo1(x bound in phi)
1bv-¬2(x bound in lnotphi)
2imgen>3(forallx(lnotphitopsi)leftrightarrow(lnotphitoforallxpsi))
df-or4((phiveepsi)leftrightarrow(lnotphitopsi))
4eqt-∀-i5(forallx(phiveepsi)leftrightarrowforallx(lnotphitopsi))
df-or6((phiveeforallxpsi)leftrightarrow(lnotphitoforallxpsi))
3, 5, 6<2bitr7(forallx(phiveepsi)leftrightarrow(phiveeforallxpsi))