Theorem nfsuc 4386

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

Hypothesis

Ref	Expression
nfsuc.1	|- F/_ x A

Assertion

Ref	Expression
nfsuc	|- F/_ x suc A

Proof of Theorem nfsuc

Step	Hyp	Ref	Expression
1		df-suc 4349	. 2 |- suc A = ( A u. { A } )
2		nfsuc.1	. . 3 |- F/_ x A
3	2	nfsn 3636	. . 3 |- F/_ x { A }
4	2, 3	nfun 3278	. 2 |- F/_ x ( A u. { A } )
5	1, 4	nfcxfr 2305	1 |- F/_ x suc A

Syntax hints:   F/_wnfc 2295   u. cun 3114   {csn 3576   suc csuc 4343

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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583  df-suc 4349

This theorem is referenced by: (None)