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Theorem nfopd 3608
 Description: Deduction version of bound-variable hypothesis builder nfop 3607. This shows how the deduction version of a not-free theorem such as nfop 3607 can be created from the corresponding not-free inference theorem. (Contributed by NM, 4-Feb-2008.)
Hypotheses
Ref Expression
nfopd.2
nfopd.3
Assertion
Ref Expression
nfopd

Proof of Theorem nfopd
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfaba1 2228 . . 3
2 nfaba1 2228 . . 3
31, 2nfop 3607 . 2
4 nfopd.2 . . 3
5 nfopd.3 . . 3
6 nfnfc1 2226 . . . . 5
7 nfnfc1 2226 . . . . 5
86, 7nfan 1498 . . . 4
9 abidnf 2770 . . . . . 6
109adantr 270 . . . . 5
11 abidnf 2770 . . . . . 6
1211adantl 271 . . . . 5
1310, 12opeq12d 3599 . . . 4
148, 13nfceqdf 2222 . . 3
154, 5, 14syl2anc 403 . 2
163, 15mpbii 146 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283   wceq 1285   wcel 1434  cab 2069  wnfc 2210  cop 3420 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2987  df-sn 3423  df-pr 3424  df-op 3426 This theorem is referenced by:  nfbrd  3849  nfovd  5586
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