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Theorem dvelimdf 2071
 Description: Deduction form of dvelimf 2069. This version may be useful if we want to avoid ax-17 1627 and use ax-16 2223 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.1 . . . 4
2 dvelimdf.3 . . . 4
31, 2nfim1 1831 . . 3
4 dvelimdf.2 . . . 4
5 dvelimdf.4 . . . 4
64, 5nfim1 1831 . . 3
7 dvelimdf.5 . . . . 5
87com12 30 . . . 4
98pm5.74d 240 . . 3
103, 6, 9dvelimf 2069 . 2
11 pm5.5 328 . . 3
121, 11nfbidf 1791 . 2
1310, 12syl5ib 212 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wal 1550  wnf 1554 This theorem is referenced by:  nfsb4t  2129  dvelimdc  2594 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 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555
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