Theorem nffvd 5880

Description: Deduction version of bound-variable hypothesis builder nffv 5878. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 15-Oct-2016.)

Hypotheses

Ref	Expression
nffvd.2
nffvd.3

Assertion

Ref	Expression
nffvd

Proof of Theorem nffvd

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfaba1 2624	. . 3
2		nfaba1 2624	. . 3
3	1, 2	nffv 5878	. 2
4		nffvd.2	. . 3
5		nffvd.3	. . 3
6		nfnfc1 2622	. . . . 5
7		nfnfc1 2622	. . . . 5
8	6, 7	nfan 1928	. . . 4
9		abidnf 3268	. . . . . 6
10	9	adantr 465	. . . . 5
11		abidnf 3268	. . . . . 6
12	11	adantl 466	. . . . 5
13	10, 12	fveq12d 5877	. . . 4
14	8, 13	nfceqdf 2614	. . 3
15	4, 5, 14	syl2anc 661	. 2
16	3, 15	mpbii 211	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442  F/_wnfc 2605  `cfv 5593

This theorem is referenced by:  nfovd  6321  nfixp  7508

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-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-iota 5556  df-fv 5601