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Theorem nfabd2 2589
 Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
nfabd2.1
nfabd2.2
Assertion
Ref Expression
nfabd2

Proof of Theorem nfabd2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1629 . . . 4
2 df-clab 2422 . . . . 5
3 nfabd2.1 . . . . . . 7
4 nfnae 2044 . . . . . . 7
53, 4nfan 1846 . . . . . 6
6 nfabd2.2 . . . . . 6
75, 6nfsbd 2186 . . . . 5
82, 7nfxfrd 1580 . . . 4
91, 8nfcd 2566 . . 3
109ex 424 . 2
11 nfab1 2573 . . 3
12 eqidd 2436 . . . 4
1312drnfc1 2587 . . 3
1411, 13mpbiri 225 . 2
1510, 14pm2.61d2 154 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wnf 1553  wsb 1658   wcel 1725  cab 2421  wnfc 2558 This theorem is referenced by:  nfabd  2590  nfrab  2881  nfriotad  6550  nfixp  7073 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-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560
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