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Theorem nfsuc 4654
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 4589 . 2  |-  suc  A  =  ( A  u.  { A } )
2 nfsuc.1 . . 3  |-  F/_ x A
32nfsn 3868 . . 3  |-  F/_ x { A }
42, 3nfun 3505 . 2  |-  F/_ x
( A  u.  { A } )
51, 4nfcxfr 2571 1  |-  F/_ x  suc  A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2561    u. cun 3320   {csn 3816   suc csuc 4585
This theorem is referenced by:  rankidb  7728  dfon2lem3  25414
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-sn 3822  df-pr 3823  df-suc 4589
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