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Theorem nfifd 3764
 Description: Deduction version of nfif 3765. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
nfifd.2
nfifd.3
nfifd.4
Assertion
Ref Expression
nfifd

Proof of Theorem nfifd
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfif2 3743 . 2
2 nfv 1630 . . 3
3 nfifd.4 . . . . . 6
43nfcrd 2587 . . . . 5
5 nfifd.2 . . . . 5
64, 5nfimd 1828 . . . 4
7 nfifd.3 . . . . . 6
87nfcrd 2587 . . . . 5
98, 5nfand 1844 . . . 4
106, 9nfimd 1828 . . 3
112, 10nfabd 2593 . 2
121, 11nfcxfrd 2572 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wnf 1554   wcel 1726  cab 2424  wnfc 2561  cif 3741 This theorem is referenced by:  nfif  3765  nfriotad  6560 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-or 361  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  df-if 3742
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