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Theorem nfsuc 4391
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 4354 . 2  |-  suc  A  =  ( A  u.  { A } )
2 nfsuc.1 . . 3  |-  F/_ x A
32nfsn 3641 . . 3  |-  F/_ x { A }
42, 3nfun 3283 . 2  |-  F/_ x
( A  u.  { A } )
51, 4nfcxfr 2309 1  |-  F/_ x  suc  A
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2299    u. cun 3119   {csn 3581   suc csuc 4348
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-sn 3587  df-pr 3588  df-suc 4354
This theorem is referenced by: (None)
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