dral1

Theorem.

Arguments:

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

Hypotheses:

(forallx(xeqy)to(phileftrightarrowpsi))

Assertions:

(forallx(xeqy)to(forallxphileftrightarrowforallypsi))

Proof:

Hyp Ref Line Expr
Hypo1(forallx(xeqy)to(phileftrightarrowpsi))
1bi>2(forallx(xeqy)to(phitopsi))
22im.bldal3(forallxforallx(xeqy)to(forallxphitoforallxpsi))
bv-idvar4(x bound in forallx(xeqy))
3, 4bvsyl5(forallx(xeqy)to(forallxphitoforallxpsi))
ax106(forallx(xeqy)to(forallxpsitoforallypsi))
5, 6syld7(forallx(xeqy)to(forallxphitoforallypsi))
1bi<8(forallx(xeqy)to(psitophi))
82im.bldal9(forallyforallx(xeqy)to(forallypsitoforallyphi))
bv-idvar10(y bound in forallx(xeqy))
9, 10bvsyl11(forallx(xeqy)to(forallypsitoforallyphi))
ax1012(forally(yeqx)to(forallyphitoforallxphi))
12aleqcom13(forallx(xeqy)to(forallyphitoforallxphi))
11, 13syld14(forallx(xeqy)to(forallypsitoforallxphi))
7, 14>bid15(forallx(xeqy)to(forallxphileftrightarrowforallypsi))