ax-bdsb - Mathbox for BJ

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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 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 1645	. 2 wff [𝑦 / 𝑥]𝜑
5	4	wbd 9932	1 wff BOUNDED [𝑦 / 𝑥]𝜑

Colors of variables: wff set class

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

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