Axiom ax-bdex 15465

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 1363	. . 3 class 𝑦
5	1, 2, 4	wrex 2476	. 2 wff ∃𝑥 ∈ 𝑦 𝜑
6	5	wbd 15458	1 wff BOUNDED ∃𝑥 ∈ 𝑦 𝜑

This axiom is referenced by:  bj-bdcel  15483  bdreu  15501  bdrmo  15502  bdcuni  15522  bdciun  15524  bj-axun2  15561  bj-nn0suc0  15596