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Theorem nfsbd 1989
Description: Deduction version of nfsb 1958. (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 1530 . 2  |-  ( ph  ->  A. x ph )
3 nfsbd.2 . . 3  |-  ( ph  ->  F/ z ps )
43alimi 1466 . 2  |-  ( A. x ph  ->  A. x F/ z ps )
5 nfsbt 1988 . 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 1362   F/wnf 1471   [wsb 1773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774
This theorem is referenced by:  nfeud  2054  nfabd  2352  nfraldya  2525  nfrexdya  2526  cbvrald  15018
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