Axiom ax-bdal 13005

Description: A bounded universal quantification of a bounded formula is bounded. Note the disjoint variable condition on x , y. (Contributed by BJ, 25-Sep-2019.)

Hypothesis

Ref	Expression
bdal.1	|- BOUNDED ph

Assertion

Ref	Expression
ax-bdal	|- BOUNDED A. x e. y ph

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Detailed syntax breakdown of Axiom ax-bdal

Step	Hyp	Ref	Expression
1		wph	. . 3 wff ph
2		vx	. . 3 setvar x
3		vy	. . . 4 setvar y
4	3	cv 1330	. . 3 class y
5	1, 2, 4	wral 2414	. 2 wff A. x e. y ph
6	5	wbd 12999	1 wff BOUNDED A. x e. y ph

This axiom is referenced by:  bdreu  13042  bdss  13051  bdcint  13064  bdciin  13066  bdcriota  13070  bj-bdind  13117  bj-nntrans  13138