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Theorem nfsuc 4325
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 4288 . 2 suc 𝐴 = (𝐴 ∪ {𝐴})
2 nfsuc.1 . . 3 𝑥𝐴
32nfsn 3578 . . 3 𝑥{𝐴}
42, 3nfun 3227 . 2 𝑥(𝐴 ∪ {𝐴})
51, 4nfcxfr 2276 1 𝑥 suc 𝐴
Colors of variables: wff set class
Syntax hints:  wnfc 2266  cun 3064  {csn 3522  suc csuc 4282
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-suc 4288
This theorem is referenced by: (None)
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