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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.
StepHypRef Expression
1 nfaba1 2624 . . 3
2 nfaba1 2624 . . 3
31, 2nffv 5878 . 2
4 nffvd.2 . . 3
5 nffvd.3 . . 3
6 nfnfc1 2622 . . . . 5
7 nfnfc1 2622 . . . . 5
86, 7nfan 1928 . . . 4
9 abidnf 3268 . . . . . 6
109adantr 465 . . . . 5
11 abidnf 3268 . . . . . 6
1211adantl 466 . . . . 5
1310, 12fveq12d 5877 . . . 4
148, 13nfceqdf 2614 . . 3
154, 5, 14syl2anc 661 . 2
163, 15mpbii 211 1
Colors of variables: wff setvar class
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
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