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Theorem nfim1 2022
Description: A closed form of nfim 2023. (Contributed by NM, 2-Jun-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 2-Jan-2018.)
Hypotheses
Ref Expression
nfim1.1  |-  F/ x ph
nfim1.2  |-  ( ph  ->  F/ x ps )
Assertion
Ref Expression
nfim1  |-  F/ x
( ph  ->  ps )

Proof of Theorem nfim1
StepHypRef Expression
1 nfim1.1 . . . 4  |-  F/ x ph
21nfri 1972 . . 3  |-  ( ph  ->  A. x ph )
3 nfim1.2 . . . 4  |-  ( ph  ->  F/ x ps )
43nfrd 1973 . . 3  |-  ( ph  ->  ( ps  ->  A. x ps ) )
52, 4hbim1 2021 . 2  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )
65nfi 1682 1  |-  F/ x
( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   F/wnf 1675
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-ex 1672  df-nf 1676
This theorem is referenced by:  nfim  2023  cbv1  2123  dvelimdf  2184  sbied  2258  sbco2d  2265  bj-cbv1v  31396
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