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Theorem dvelimdf 2082
Description: Deduction form of dvelimf 1997. This version may be useful if we want to avoid ax-17 1616 and use ax-16 2144 instead. (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypotheses
Ref Expression
dvelimdf.1  F/
dvelimdf.2  F/
dvelimdf.3  F/
dvelimdf.4  F/
dvelimdf.5
Assertion
Ref Expression
dvelimdf  F/

Proof of Theorem dvelimdf
StepHypRef Expression
1 dvelimdf.2 . . . . . 6  F/
2 dvelimdf.3 . . . . . 6  F/
31, 2alrimi 1765 . . . . 5  F/
4 nfsb4t 2080 . . . . 5  F/  F/
53, 4syl 15 . . . 4  F/
65imp 418 . . 3  F/
7 dvelimdf.1 . . . . 5  F/
8 nfnae 1956 . . . . 5  F/
97, 8nfan 1824 . . . 4  F/
10 dvelimdf.4 . . . . . 6  F/
11 dvelimdf.5 . . . . . 6
121, 10, 11sbied 2036 . . . . 5
1312adantr 451 . . . 4
149, 13nfbidf 1774 . . 3  F/  F/
156, 14mpbid 201 . 2  F/
1615ex 423 1  F/
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1540   F/wnf 1544  wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by:  dvelimdc  2509
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