Theorem nfsuc 4422

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 4385	. 2 |- suc A = ( A u. { A } )
2		nfsuc.1	. . 3 |- F/_ x A
3	2	nfsn 3666	. . 3 |- F/_ x { A }
4	2, 3	nfun 3305	. 2 |- F/_ x ( A u. { A } )
5	1, 4	nfcxfr 2328	1 |- F/_ x suc A

Syntax hints:   F/_wnfc 2318   u. cun 3141   {csn 3606   suc csuc 4379

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 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2170

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2175  df-cleq 2181  df-clel 2184  df-nfc 2320  df-v 2753  df-un 3147  df-sn 3612  df-pr 3613  df-suc 4385

This theorem is referenced by: (None)