Theorem nfsuc 4330

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 4293	. 2 |- suc A = ( A u. { A } )
2		nfsuc.1	. . 3 |- F/_ x A
3	2	nfsn 3583	. . 3 |- F/_ x { A }
4	2, 3	nfun 3232	. 2 |- F/_ x ( A u. { A } )
5	1, 4	nfcxfr 2278	1 |- F/_ x suc A

Syntax hints:   F/_wnfc 2268   u. cun 3069   {csn 3527   suc csuc 4287

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-suc 4293

This theorem is referenced by: (None)