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Theorem nfabd2 2592
 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 1630 . . . 4
2 df-clab 2425 . . . . 5
3 nfabd2.1 . . . . . . 7
4 nfnae 2045 . . . . . . 7
53, 4nfan 1847 . . . . . 6
6 nfabd2.2 . . . . . 6
75, 6nfsbd 2189 . . . . 5
82, 7nfxfrd 1581 . . . 4
91, 8nfcd 2569 . . 3
109ex 425 . 2
11 nfab1 2576 . . 3
12 eqidd 2439 . . . 4
1312drnfc1 2590 . . 3
1411, 13mpbiri 226 . 2
1510, 14pm2.61d2 155 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360  wal 1550  wnf 1554  wsb 1659   wcel 1726  cab 2424  wnfc 2561 This theorem is referenced by:  nfabd  2593  nfrab  2891  nfriotad  6561  nfixp  7084 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563
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