Axiom ax-bdsb 9942

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 1646, nor probably any other equivalent formula, is syntactically bounded. (Contributed by BJ, 3-Oct-2019.)

Hypothesis

Ref	Expression
bdsb.1	|- BOUNDED ph

Assertion

Ref	Expression
ax-bdsb	|- BOUNDED [ y / x ] ph

Detailed syntax breakdown of Axiom ax-bdsb

Step	Hyp	Ref	Expression
1		wph	. . 3 wff ph
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4	1, 2, 3	wsb 1645	. 2 wff [ y / x ] ph
5	4	wbd 9932	1 wff BOUNDED [ y / x ] ph

This axiom is referenced by:  bdab  9958  bdph  9970  bdsbc  9978  bdcriota  10003