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Axiom ax-bdsb 10329
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 1662, 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
StepHypRef Expression
1 wph . . 3 wff 𝜑
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
41, 2, 3wsb 1661 . 2 wff [𝑦 / 𝑥]𝜑
54wbd 10319 1 wff BOUNDED [𝑦 / 𝑥]𝜑
Colors of variables: wff set class
This axiom is referenced by:  bdab  10345  bdph  10357  bdsbc  10365  bdcriota  10390
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