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Theorem dvelimdf 1892
 Description: Deduction form of dvelimf 1891. This version may be useful if we want to avoid ax-17 1419 and use ax-16 1695 instead. (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 11-May-2018.)
Hypotheses
Ref Expression
dvelimdf.1
dvelimdf.2
dvelimdf.3
dvelimdf.4
dvelimdf.5
Assertion
Ref Expression
dvelimdf

Proof of Theorem dvelimdf
StepHypRef Expression
1 dvelimdf.2 . . . 4
2 dvelimdf.3 . . . 4
31, 2alrimi 1415 . . 3
4 nfsb4t 1890 . . 3
53, 4syl 14 . 2
6 dvelimdf.1 . . 3
7 dvelimdf.4 . . . 4
8 dvelimdf.5 . . . 4
91, 7, 8sbied 1671 . . 3
106, 9nfbidf 1432 . 2
115, 10sylibd 138 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 98  wal 1241  wnf 1349  wsb 1645 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646 This theorem is referenced by:  dvelimdc  2197
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