Axiom ax-bdex 7193

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 1227	. . 3 class y
5	1, 2, 4	wrex 2285	. 2 wff ∃x ∈ y φ
6	5	wbd 7186	1 wff BOUNDED ∃x ∈ y φ

This axiom is referenced by:  bj-bdcel  7211  bdreu  7229  bdrmo  7230  bdcuni  7250  bdciun  7252  bj-axun2  7285  bj-nn0suc0  7319