cbv-∃1

Theorem.

Arguments:

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

Distinct variable conditions:

(x, y),

Hypotheses:

((xeqy)to(phileftrightarrowpsi))
(x bound in psi)
(y bound in phi)

Assertions:

(_e1xphileftrightarrow_e1ypsi)

Proof:

Hyp Ref Line Expr
Hypo1((xeqy)to(phileftrightarrowpsi))
2(x bound in psi)
3(y bound in phi)
3chvar-∃14(_e1xphileftrightarrow_e1y[y/x]phi)
1, 2sb-xpl5([y/x]phileftrightarrowpsi)
5eqt-∃1-i6(_e1y[y/x]phileftrightarrow_e1ypsi)
4, 6bitr7(_e1xphileftrightarrow_e1ypsi)