Theorem nfsuc 4511

Description: Bound-variable hypothesis builder for successor. (Contributed by NM, 15-Sep-2003.)

Hypothesis

Ref	Expression
nfsuc.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfsuc	⊢ Ⅎ𝑥 suc 𝐴

Proof of Theorem nfsuc

Step	Hyp	Ref	Expression
1		df-suc 4474	. 2 ⊢ suc 𝐴 = (𝐴 ∪ {𝐴})
2		nfsuc.1	. . 3 ⊢ Ⅎ𝑥𝐴
3	2	nfsn 3733	. . 3 ⊢ Ⅎ𝑥{𝐴}
4	2, 3	nfun 3365	. 2 ⊢ Ⅎ𝑥(𝐴 ∪ {𝐴})
5	1, 4	nfcxfr 2372	1 ⊢ Ⅎ𝑥 suc 𝐴

Syntax hints:  Ⅎwnfc 2362   ∪ cun 3199  {csn 3673  suc csuc 4468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-un 3205  df-sn 3679  df-pr 3680  df-suc 4474

This theorem is referenced by: (None)