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Theorem dvelimdf 2022
 Description: Deduction form of dvelimf 1937. This version may be useful if we want to avoid ax-17 1603 and use ax-16 2083 instead. (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 6-Oct-2016.)
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 . . . . . 6
2 dvelimdf.3 . . . . . 6
31, 2alrimi 1745 . . . . 5
4 nfsb4t 2020 . . . . 5
53, 4syl 15 . . . 4
65imp 418 . . 3
7 dvelimdf.1 . . . . 5
8 nfnae 1896 . . . . 5
97, 8nfan 1771 . . . 4
10 dvelimdf.4 . . . . . 6
11 dvelimdf.5 . . . . . 6
121, 10, 11sbied 1976 . . . . 5
1312adantr 451 . . . 4
149, 13nfbidf 1754 . . 3
156, 14mpbid 201 . 2
1615ex 423 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1527  wnf 1531  wsb 1629 This theorem is referenced by:  dvelimdc  2439 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630
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