Axiom ax-bdex 16140

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 1394	. . 3 class y
5	1, 2, 4	wrex 2509	. 2 wff E. x e. y ph
6	5	wbd 16133	1 wff BOUNDED E. x e. y ph

This axiom is referenced by:  bj-bdcel  16158  bdreu  16176  bdrmo  16177  bdcuni  16197  bdciun  16199  bj-axun2  16236  bj-nn0suc0  16271