Theorem nfsuc 4473

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 4436	. 2 |- suc A = ( A u. { A } )
2		nfsuc.1	. . 3 |- F/_ x A
3	2	nfsn 3703	. . 3 |- F/_ x { A }
4	2, 3	nfun 3337	. 2 |- F/_ x ( A u. { A } )
5	1, 4	nfcxfr 2347	1 |- F/_ x suc A

Syntax hints:   F/_wnfc 2337   u. cun 3172   {csn 3643   suc csuc 4430

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-un 3178  df-sn 3649  df-pr 3650  df-suc 4436

This theorem is referenced by: (None)