MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfsuc Structured version   Visualization version   GIF version

Theorem nfsuc 6249
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 6184 . 2 suc 𝐴 = (𝐴 ∪ {𝐴})
2 nfsuc.1 . . 3 𝑥𝐴
32nfsn 4628 . . 3 𝑥{𝐴}
42, 3nfun 4127 . 2 𝑥(𝐴 ∪ {𝐴})
51, 4nfcxfr 2980 1 𝑥 suc 𝐴
Colors of variables: wff setvar class
Syntax hints:  wnfc 2962  cun 3917  {csn 4550  suc csuc 6180
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-v 3482  df-un 3924  df-sn 4551  df-pr 4553  df-suc 6184
This theorem is referenced by:  rankidb  9226  dfon2lem3  33087
  Copyright terms: Public domain W3C validator