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Theorem nfsbd 1867
Description: Deduction version of nfsb 1838. (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 1428 . 2  |-  ( ph  ->  A. x ph )
3 nfsbd.2 . . 3  |-  ( ph  ->  F/ z ps )
43alimi 1360 . 2  |-  ( A. x ph  ->  A. x F/ z ps )
5 nfsbt 1866 . 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 1257   F/wnf 1365   [wsb 1661
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662
This theorem is referenced by:  nfeud  1932  nfabd  2212  nfraldya  2375  nfrexdya  2376  cbvrald  10314
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