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Theorem nfsuc 5713
 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 5646 . 2 suc 𝐴 = (𝐴 ∪ {𝐴})
2 nfsuc.1 . . 3 𝑥𝐴
32nfsn 4189 . . 3 𝑥{𝐴}
42, 3nfun 3731 . 2 𝑥(𝐴 ∪ {𝐴})
51, 4nfcxfr 2749 1 𝑥 suc 𝐴
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2738   ∪ cun 3538  {csn 4125  suc csuc 5642 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-sn 4126  df-pr 4128  df-suc 5646 This theorem is referenced by:  rankidb  8546  dfon2lem3  30934
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