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Theorem nfopd 3993
 Description: Deduction version of bound-variable hypothesis builder nfop 3992. This shows how the deduction version of a not-free theorem such as nfop 3992 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 2576 . . 3
2 nfaba1 2576 . . 3
31, 2nfop 3992 . 2
4 nfopd.2 . . 3
5 nfopd.3 . . 3
6 nfnfc1 2574 . . . . 5
7 nfnfc1 2574 . . . . 5
86, 7nfan 1846 . . . 4
9 abidnf 3095 . . . . . 6
109adantr 452 . . . . 5
11 abidnf 3095 . . . . . 6
1211adantl 453 . . . . 5
1310, 12opeq12d 3984 . . . 4
148, 13nfceqdf 2570 . . 3
154, 5, 14syl2anc 643 . 2
163, 15mpbii 203 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wceq 1652   wcel 1725  cab 2421  wnfc 2558  cop 3809 This theorem is referenced by:  nfbrd  4247  dfid3  4491  nfovd  6095 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815
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