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Theorem nfsbd 1951
Description: Deduction version of nfsb 1920. (Contributed by NM, 15-Feb-2013.)
Hypotheses
Ref Expression
nfsbd.1  |-  F/ x ph
nfsbd.2  |-  ( ph  ->  F/ z ps )
Assertion
Ref Expression
nfsbd  |-  ( ph  ->  F/ z [ y  /  x ] ps )
Distinct variable group:    y, z
Allowed substitution hints:    ph( x, y, z)    ps( x, y, z)

Proof of Theorem nfsbd
StepHypRef Expression
1 nfsbd.1 . . 3  |-  F/ x ph
21nfri 1500 . 2  |-  ( ph  ->  A. x ph )
3 nfsbd.2 . . 3  |-  ( ph  ->  F/ z ps )
43alimi 1432 . 2  |-  ( A. x ph  ->  A. x F/ z ps )
5 nfsbt 1950 . 2  |-  ( A. x F/ z ps  ->  F/ z [ y  /  x ] ps )
62, 4, 53syl 17 1  |-  ( ph  ->  F/ z [ y  /  x ] ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1330   F/wnf 1437   [wsb 1736
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737
This theorem is referenced by:  nfeud  2016  nfabd  2301  nfraldya  2472  nfrexdya  2473  cbvrald  13166
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