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Theorem bj-nfv 31006
Description: A non-occurring variable is semantically non-free. (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
bj-nfv  |- FF/ x ph
Distinct variable group:    ph, x

Proof of Theorem bj-nfv
StepHypRef Expression
1 ax5e 1753 . . 3  |-  ( E. x ph  ->  ph )
2 ax-5 1751 . . 3  |-  ( ph  ->  A. x ph )
31, 2syl 17 . 2  |-  ( E. x ph  ->  A. x ph )
4 df-bj-nf 30974 . 2  |-  (FF/ x
ph 
<->  ( E. x ph  ->  A. x ph )
)
53, 4mpbir 212 1  |- FF/ x ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   E.wex 1659  FF/wnff 30973
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-5 1751
This theorem depends on definitions:  df-bi 188  df-ex 1660  df-bj-nf 30974
This theorem is referenced by: (None)
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