sb-bvw

Theorem.

Arguments:

a (st), x (sv), phi (pr),

Distinct variable conditions:

(a, x),

Hypotheses:

(x bound in phi)

Assertions:

([a/x]phileftrightarrowphi)

Proof:

Hyp Ref Line Expr
Hypo1(x bound in phi)
dfsb-dvex2([a/x]phileftrightarrowexistsx((xeqa)wedgephi))
1exan>3(existsx((xeqa)wedgephi)leftrightarrow(existsx(xeqa)wedgephi))
2, 3bitr4([a/x]phileftrightarrow(existsx(xeqa)wedgephi))
ax9ex5existsx(xeqa)
5an-true<6(phileftrightarrow(existsx(xeqa)wedgephi))
4, 6><bitr7([a/x]phileftrightarrowphi)