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Axiom ax-bdal 9253
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 φ
Assertion
Ref Expression
ax-bdal BOUNDED x y φ
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)

Detailed syntax breakdown of Axiom ax-bdal
StepHypRef Expression
1 wph . . 3 wff φ
2 vx . . 3 setvar x
3 vy . . . 4 setvar y
43cv 1241 . . 3 class y
51, 2, 4wral 2300 . 2 wff x y φ
65wbd 9247 1 wff BOUNDED x y φ
Colors of variables: wff set class
This axiom is referenced by:  bdreu  9290  bdss  9299  bdcint  9312  bdciin  9314  bdcriota  9318  bj-bdind  9365  bj-nntrans  9385
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