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Axiom ax-bdsb 7196
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 1628, 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 1627 . 2 wff [y / x]φ
54wbd 7186 1 wff BOUNDED [y / x]φ
Colors of variables: wff set class
This axiom is referenced by:  bdab  7212  bdph  7224  bdsbc  7232  bdcriota  7257
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