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Theorem nfabd2 2640
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 1707 . . . 4
2 df-clab 2443 . . . . 5
3 nfabd2.1 . . . . . . 7
4 nfnae 2058 . . . . . . 7
53, 4nfan 1928 . . . . . 6
6 nfabd2.2 . . . . . 6
75, 6nfsbd 2186 . . . . 5
82, 7nfxfrd 1646 . . . 4
91, 8nfcd 2613 . . 3
109ex 434 . 2
11 nfab1 2621 . . 3
12 eqidd 2458 . . . 4
1312drnfc1 2638 . . 3
1411, 13mpbiri 233 . 2
1510, 14pm2.61d2 160 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  F/wnf 1616  [wsb 1739  e.wcel 1818  {cab 2442  F/_wnfc 2605
This theorem is referenced by:  nfabd  2641  nfrab  3039  nfixp  7508
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607
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