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Theorem nfsbd 1911
Description: Deduction version of nfsb 1882. (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 1467 . 2  |-  ( ph  ->  A. x ph )
3 nfsbd.2 . . 3  |-  ( ph  ->  F/ z ps )
43alimi 1399 . 2  |-  ( A. x ph  ->  A. x F/ z ps )
5 nfsbt 1910 . 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 1297   F/wnf 1404   [wsb 1703
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483
This theorem depends on definitions:  df-bi 116  df-nf 1405  df-sb 1704
This theorem is referenced by:  nfeud  1976  nfabd  2259  nfraldya  2428  nfrexdya  2429  cbvrald  12576
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