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Axiom ax-bdex 12828
Description: A bounded existential quantification of a bounded formula is bounded. Note the disjoint variable condition on  x ,  y. (Contributed by BJ, 25-Sep-2019.)
Hypothesis
Ref Expression
bdal.1  |- BOUNDED  ph
Assertion
Ref Expression
ax-bdex  |- BOUNDED  E. x  e.  y 
ph
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Detailed syntax breakdown of Axiom ax-bdex
StepHypRef Expression
1 wph . . 3  wff  ph
2 vx . . 3  setvar  x
3 vy . . . 4  setvar  y
43cv 1313 . . 3  class  y
51, 2, 4wrex 2392 . 2  wff  E. x  e.  y  ph
65wbd 12821 1  wff BOUNDED  E. x  e.  y 
ph
Colors of variables: wff set class
This axiom is referenced by:  bj-bdcel  12846  bdreu  12864  bdrmo  12865  bdcuni  12885  bdciun  12887  bj-axun2  12924  bj-nn0suc0  12959
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