bv-=

Theorem.

Arguments:

a (coll), b (coll), x (sv),

Dummy variables:

y (sv),

Distinct variable conditions:

(y, a), (y, b), (y, x),

Hypotheses:

(x bound in b)
(x bound in a)

Assertions:

(x bound in (aequivb))

Proof:

Hyp Ref Line Expr
Hypo1(x bound in b)
2(x bound in a)
2df-bvt3(x bound in (yina))
1df-bvt4(x bound in (yinb))
3, 4bv-↔5(x bound in ((yina)leftrightarrow(yinb)))
5bv-∀6(x bound in forally((yina)leftrightarrow(yinb)))
df-equ7((aequivb)leftrightarrowforally((yina)leftrightarrow(yinb)))
6, 7bvdef8(x bound in (aequivb))