Theorem nfsuc 5796

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 5729	. 2 |- suc A = ( A u. { A } )
2		nfsuc.1	. . 3 |- F/_ x A
3	2	nfsn 4242	. . 3 |- F/_ x { A }
4	2, 3	nfun 3769	. 2 |- F/_ x ( A u. { A } )
5	1, 4	nfcxfr 2762	1 |- F/_ x suc A

Syntax hints:   F/_wnfc 2751   u. cun 3572   {csn 4177   suc csuc 5725

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-un 3579  df-sn 4178  df-pr 4180  df-suc 5729

This theorem is referenced by:  rankidb  8663  dfon2lem3  31690