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Axiom ax-bdal 11178
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 BOUNDED𝑥𝑦 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 1286 . . 3 class 𝑦
51, 2, 4wral 2355 . 2 wff 𝑥𝑦 𝜑
65wbd 11172 1 wff BOUNDED𝑥𝑦 𝜑
Colors of variables: wff set class
This axiom is referenced by:  bdreu  11215  bdss  11224  bdcint  11237  bdciin  11239  bdcriota  11243  bj-bdind  11294  bj-nntrans  11315
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