Axiom ax-bdsb 9257

Description: A formula resulting from proper substitution in a bounded formula is bounded. This probably cannot be proved from the other axioms, since neither the definiens in df-sb 1643, nor probably any other equivalent formula, is syntactically bounded. (Contributed by BJ, 3-Oct-2019.)

Hypothesis

Ref	Expression
bdsb.1	⊢ BOUNDED φ

Assertion

Ref	Expression
ax-bdsb	⊢ BOUNDED [y / x]φ

Detailed syntax breakdown of Axiom ax-bdsb

Step	Hyp	Ref	Expression
1		wph	. . 3 wff φ
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4	1, 2, 3	wsb 1642	. 2 wff [y / x]φ
5	4	wbd 9247	1 wff BOUNDED [y / x]φ

This axiom is referenced by:  bdab  9273  bdph  9285  bdsbc  9293  bdcriota  9318