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Theorem nfsuc 5981
Description: Bound-variable hypothesis builder for successor. (Contributed by NM, 15-Sep-2003.)
Hypothesis
Ref Expression
nfsuc.1 𝑥𝐴
Assertion
Ref Expression
nfsuc 𝑥 suc 𝐴

Proof of Theorem nfsuc
StepHypRef Expression
1 df-suc 5916 . 2 suc 𝐴 = (𝐴 ∪ {𝐴})
2 nfsuc.1 . . 3 𝑥𝐴
32nfsn 4400 . . 3 𝑥{𝐴}
42, 3nfun 3933 . 2 𝑥(𝐴 ∪ {𝐴})
51, 4nfcxfr 2905 1 𝑥 suc 𝐴
Colors of variables: wff setvar class
Syntax hints:  wnfc 2894  cun 3732  {csn 4336  suc csuc 5912
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-13 2352  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-nfc 2896  df-v 3352  df-un 3739  df-sn 4337  df-pr 4339  df-suc 5916
This theorem is referenced by:  rankidb  8882  dfon2lem3  32154
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