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Axiom ax-bdal 10794
Description: A bounded universal quantification of a bounded formula is bounded. Note the DV condition on  x ,  y. (Contributed by BJ, 25-Sep-2019.)
Hypothesis
Ref Expression
bdal.1  |- BOUNDED  ph
Assertion
Ref Expression
ax-bdal  |- BOUNDED  A. x  e.  y 
ph
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Detailed syntax breakdown of Axiom ax-bdal
StepHypRef Expression
1 wph . . 3  wff  ph
2 vx . . 3  setvar  x
3 vy . . . 4  setvar  y
43cv 1284 . . 3  class  y
51, 2, 4wral 2349 . 2  wff  A. x  e.  y  ph
65wbd 10788 1  wff BOUNDED  A. x  e.  y 
ph
Colors of variables: wff set class
This axiom is referenced by:  bdreu  10831  bdss  10840  bdcint  10853  bdciin  10855  bdcriota  10859  bj-bdind  10910  bj-nntrans  10931
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