∃1→∃mo-0

Theorem.

Arguments:

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

Distinct variable conditions:

(x, y),

Hypotheses:

(y bound in phi)

Assertions:

(_e1xphitoexistsyforallx(phito(xeqy)))

Proof:

Hyp Ref Line Expr
Hypo1(y bound in phi)
1df-∃1-alt2(_e1xphileftrightarrowexistsyforallx(phileftrightarrow(xeqy)))
bi>3((phileftrightarrow(xeqy))to(phito(xeqy)))
3im.bldal4(forallx(phileftrightarrow(xeqy))toforallx(phito(xeqy)))
4im.bldex5(existsyforallx(phileftrightarrow(xeqy))toexistsyforallx(phito(xeqy)))
2, 5brpi216(_e1xphitoexistsyforallx(phito(xeqy)))