Theorem nfsbcd 3348

Description: Deduction version of nfsbc 3349. (Contributed by NM, 23-Nov-2005.) (Revised by Mario Carneiro, 12-Oct-2016.)

Hypotheses

Ref	Expression
nfsbcd.1
nfsbcd.2
nfsbcd.3

Assertion

Ref	Expression
nfsbcd

Proof of Theorem nfsbcd

Step	Hyp	Ref	Expression
1		df-sbc 3328	. 2
2		nfsbcd.2	. . 3
3		nfsbcd.1	. . . 4
4		nfsbcd.3	. . . 4
5	3, 4	nfabd 2641	. . 3
6	2, 5	nfeld 2627	. 2
7	1, 6	nfxfrd 1646	1

Syntax hints:  ->wi 4  F/wnf 1616  e.wcel 1818  {cab 2442  F/_wnfc 2605  [.wsbc 3327

This theorem is referenced by:  nfsbc  3349  nfcsbd  3451  sbcnestgf  3839

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-sbc 3328