Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  ax-bdex Structured version   GIF version

Axiom ax-bdex 9254
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 1241 . . 3 class y
51, 2, 4wrex 2301 . 2 wff x y φ
65wbd 9247 1 wff BOUNDED x y φ
Colors of variables: wff set class
This axiom is referenced by:  bj-bdcel  9272  bdreu  9290  bdrmo  9291  bdcuni  9311  bdciun  9313  bj-axun2  9346  bj-nn0suc0  9384
  Copyright terms: Public domain W3C validator