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Theorem nfsuc 4226
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 4189 . 2 suc 𝐴 = (𝐴 ∪ {𝐴})
2 nfsuc.1 . . 3 𝑥𝐴
32nfsn 3497 . . 3 𝑥{𝐴}
42, 3nfun 3154 . 2 𝑥(𝐴 ∪ {𝐴})
51, 4nfcxfr 2225 1 𝑥 suc 𝐴
Colors of variables: wff set class
Syntax hints:  wnfc 2215  cun 2995  {csn 3441  suc csuc 4183
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3001  df-sn 3447  df-pr 3448  df-suc 4189
This theorem is referenced by: (None)
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