Axiom ax-bdex 9254

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

Hypothesis

Ref	Expression
bdal.1	⊢ BOUNDED φ

Assertion

Ref	Expression
ax-bdex	⊢ BOUNDED ∃x ∈ y φ

Distinct variable group:   x,y

Allowed substitution hints:   φ(x,y)

Detailed syntax breakdown of Axiom ax-bdex

Step	Hyp	Ref	Expression
1		wph	. . 3 wff φ
2		vx	. . 3 setvar x
3		vy	. . . 4 setvar y
4	3	cv 1241	. . 3 class y
5	1, 2, 4	wrex 2301	. 2 wff ∃x ∈ y φ
6	5	wbd 9247	1 wff BOUNDED ∃x ∈ y φ

This axiom is referenced by:  bj-bdcel  9272  bdreu  9290  bdrmo  9291  bdcuni  9311  bdciun  9313  bj-axun2  9346  bj-nn0suc0  9384