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Theorem nfabd2 2588
 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 1755 . . . 4
2 df-clab 2415 . . . . 5
3 nfabd2.1 . . . . . . 7
4 nfnae 2124 . . . . . . 7
53, 4nfan 1988 . . . . . 6
6 nfabd2.2 . . . . . 6
75, 6nfsbd 2248 . . . . 5
82, 7nfxfrd 1691 . . . 4
91, 8nfcd 2564 . . 3
109ex 435 . 2
11 nfab1 2571 . . 3
12 eqidd 2429 . . . 4
1312drnfc1 2586 . . 3
1411, 13mpbiri 236 . 2
1510, 14pm2.61d2 163 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370  wal 1435  wnf 1661  wsb 1790   wcel 1872  cab 2414  wnfc 2556 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558 This theorem is referenced by:  nfabd  2589  nfrab  2949  nfixp  7496
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