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Definition df-bj-rnf 32931
Description: Definition of restricted non-freeness. Informally, the proposition  F/ x  e.  A ph means that  ph ( x ) does not vary on  A. (Contributed by BJ, 19-Mar-2021.)
Assertion
Ref Expression
df-bj-rnf  |-  ( F/ x  e.  A ph  <->  ( E. x  e.  A  ph 
->  A. x  e.  A  ph ) )

Detailed syntax breakdown of Definition df-bj-rnf
StepHypRef Expression
1 wph . . 3  wff  ph
2 vx . . 3  setvar  x
3 cA . . 3  class  A
41, 2, 3wrnf 32930 . 2  wff  F/ x  e.  A ph
51, 2, 3wrex 2913 . . 3  wff  E. x  e.  A  ph
61, 2, 3wral 2912 . . 3  wff  A. x  e.  A  ph
75, 6wi 4 . 2  wff  ( E. x  e.  A  ph  ->  A. x  e.  A  ph )
84, 7wb 196 1  wff  ( F/ x  e.  A ph  <->  ( E. x  e.  A  ph 
->  A. x  e.  A  ph ) )
Colors of variables: wff setvar class
This definition is referenced by: (None)
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