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Theorem nfsbd 1851
Description: Deduction version of nfsb 1822. (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 1412 . 2  |-  ( ph  ->  A. x ph )
3 nfsbd.2 . . 3  |-  ( ph  ->  F/ z ps )
43alimi 1344 . 2  |-  ( A. x ph  ->  A. x F/ z ps )
5 nfsbt 1850 . 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 1241   F/wnf 1349   [wsb 1645
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646
This theorem is referenced by:  nfeud  1916  nfabd  2196  nfraldya  2358  nfrexdya  2359  cbvrald  9927
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