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Theorem nfsuc 5510
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 5445 . 2  |-  suc  A  =  ( A  u.  { A } )
2 nfsuc.1 . . 3  |-  F/_ x A
32nfsn 4054 . . 3  |-  F/_ x { A }
42, 3nfun 3622 . 2  |-  F/_ x
( A  u.  { A } )
51, 4nfcxfr 2582 1  |-  F/_ x  suc  A
Colors of variables: wff setvar class
Syntax hints:   F/_wnfc 2570    u. cun 3434   {csn 3996   suc csuc 5441
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-v 3083  df-un 3441  df-sn 3997  df-pr 3999  df-suc 5445
This theorem is referenced by:  rankidb  8273  dfon2lem3  30426
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