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Axiom ax-bdsb 10771
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 1687, 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
StepHypRef Expression
1 wph . . 3  wff  ph
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
41, 2, 3wsb 1686 . 2  wff  [ y  /  x ] ph
54wbd 10761 1  wff BOUNDED  [ y  /  x ] ph
Colors of variables: wff set class
This axiom is referenced by:  bdab  10787  bdph  10799  bdsbc  10807  bdcriota  10832
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