df-∃mo-alt3

Theorem.

Arguments:

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

Distinct variable conditions:

(x, y),

Hypotheses:

(y bound in phi)

Assertions:

(_em1xphileftrightarrowforallxforally((phiwedge[y/x]phi)to(xeqy)))

Proof:

Hyp Ref Line Expr
Hypo1(y bound in phi)
1df-∃mo-alt22(_em1xphileftrightarrowexistsyforallx(phito(xeqy)))
1df-∃mo-alt03(existsyforallx(phito(xeqy))leftrightarrowforallxforally((phiwedge[y/x]phi)to(xeqy)))
2, 3bitr4(_em1xphileftrightarrowforallxforally((phiwedge[y/x]phi)to(xeqy)))