Axiom ax-bdex 13017

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 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 1330	. . 3 class 𝑦
5	1, 2, 4	wrex 2417	. 2 wff ∃𝑥 ∈ 𝑦 𝜑
6	5	wbd 13010	1 wff BOUNDED ∃𝑥 ∈ 𝑦 𝜑

This axiom is referenced by:  bj-bdcel  13035  bdreu  13053  bdrmo  13054  bdcuni  13074  bdciun  13076  bj-axun2  13113  bj-nn0suc0  13148