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Axiom ax-bdex 7193
Description: A bounded existential 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-bdex BOUNDED x y φ
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)

Detailed syntax breakdown of Axiom ax-bdex
StepHypRef Expression
1 wph . . 3 wff φ
2 vx . . 3 setvar x
3 vy . . . 4 setvar y
43cv 1227 . . 3 class y
51, 2, 4wrex 2285 . 2 wff x y φ
65wbd 7186 1 wff BOUNDED x y φ
Colors of variables: wff set class
This axiom is referenced by:  bj-bdcel  7211  bdreu  7229  bdrmo  7230  bdcuni  7250  bdciun  7252  bj-axun2  7285  bj-nn0suc0  7319
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