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Theorem nfifd 3532
 Description: Deduction version of nfif 3533. (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 df-if 3506 . 2
2 nfv 1508 . . 3
3 nfifd.3 . . . . . 6
43nfcrd 2313 . . . . 5
5 nfifd.2 . . . . 5
64, 5nfand 1548 . . . 4
7 nfifd.4 . . . . . 6
87nfcrd 2313 . . . . 5
95nfnd 1637 . . . . 5
108, 9nfand 1548 . . . 4
116, 10nford 1547 . . 3
122, 11nfabd 2319 . 2
131, 12nfcxfrd 2297 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wo 698  wnf 1440   wcel 2128  cab 2143  wnfc 2286  cif 3505 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-fal 1341  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-if 3506 This theorem is referenced by:  nfif  3533
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