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Theorem nfsuc 4479
Description: Bound-variable hypothesis builder for successor. (Contributed by NM, 15-Sep-2003.)
Hypothesis
Ref Expression
nfsuc.1  |-  F/_ x A
Assertion
Ref Expression
nfsuc  |-  F/_ x  suc  A

Proof of Theorem nfsuc
StepHypRef Expression
1 df-suc 4414 . 2  |-  suc  A  =  ( A  u.  { A } )
2 nfsuc.1 . . 3  |-  F/_ x A
32nfsn 3704 . . 3  |-  F/_ x { A }
42, 3nfun 3344 . 2  |-  F/_ x
( A  u.  { A } )
51, 4nfcxfr 2429 1  |-  F/_ x  suc  A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2419    u. cun 3163   {csn 3653   suc csuc 4410
This theorem is referenced by:  rankidb  7488  dfon2lem3  24212
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-pr 3660  df-suc 4414
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