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Theorem nffvd 5330
 Description: Deduction version of bound-variable hypothesis builder nffv 5328. (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 2235 . . 3
2 nfaba1 2235 . . 3
31, 2nffv 5328 . 2
4 nffvd.2 . . 3
5 nffvd.3 . . 3
6 nfnfc1 2232 . . . . 5
7 nfnfc1 2232 . . . . 5
86, 7nfan 1503 . . . 4
9 abidnf 2784 . . . . . 6
109adantr 271 . . . . 5
11 abidnf 2784 . . . . . 6
1211adantl 272 . . . . 5
1310, 12fveq12d 5325 . . . 4
148, 13nfceqdf 2228 . . 3
154, 5, 14syl2anc 404 . 2
163, 15mpbii 147 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1288   wceq 1290   wcel 1439  cab 2075  wnfc 2216  cfv 5028 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-rex 2366  df-v 2622  df-un 3004  df-sn 3456  df-pr 3457  df-op 3459  df-uni 3660  df-br 3852  df-iota 4993  df-fv 5036 This theorem is referenced by:  nfovd  5692  nfixpxy  6488
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