ax4c1

Theorem.

Arguments:

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

Hypotheses:

((xeqy)to(phitopsi))
(chito(phitoforallxphi))
(x bound in chi)

Assertions:

(chito(phitoexistsxpsi))

Proof:

Hyp Ref Line Expr
Hypo1((xeqy)to(phitopsi))
2(chito(phitoforallxphi))
3(x bound in chi)
3df-Bvp4(chitoforallxchi)
4adan>5((chiwedgephi)toforallxchi)
2imp6((chiwedgephi)toforallxphi)
5, 6jca7((chiwedgephi)to(forallxchiwedgeforallxphi))
al.andi8(forallx(chiwedgephi)leftrightarrow(forallxchiwedgeforallxphi))
7, 8brpi22<9((chiwedgephi)toforallx(chiwedgephi))
1adan<10((xeqy)to((chiwedgephi)topsi))
9df-Bvp11(x bound in (chiwedgephi))
10, 11ax4c12((chiwedgephi)toexistsxpsi)
12exp13(chito(phitoexistsxpsi))