Axiom ax-bdex 17050

Description: A bounded existential 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-bdex	|- BOUNDED E. x e. y ph

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Detailed syntax breakdown of Axiom ax-bdex

Step	Hyp	Ref	Expression
1		wph	. . 3 wff ph
2		vx	. . 3 setvar x
3		vy	. . . 4 setvar y
4	3	cv 1401	. . 3 class y
5	1, 2, 4	wrex 2529	. 2 wff E. x e. y ph
6	5	wbd 17043	1 wff BOUNDED E. x e. y ph

This axiom is used by:  bj-bdcel  17068  bdreu  17086  bdrmo  17087  bdcuni  17107  bdciun  17109  bj-axun2  17146  bj-nn0suc0  17181