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Theorem dvelimdc 2509
 Description: Deduction form of dvelimc 2510. (Contributed by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
dvelimdc.1
dvelimdc.2
dvelimdc.3
dvelimdc.4
dvelimdc.5
Assertion
Ref Expression
dvelimdc

Proof of Theorem dvelimdc
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1619 . . 3
2 dvelimdc.1 . . . . 5
3 dvelimdc.2 . . . . 5
4 dvelimdc.3 . . . . . 6
54nfcrd 2502 . . . . 5
6 dvelimdc.4 . . . . . 6
76nfcrd 2502 . . . . 5
8 dvelimdc.5 . . . . . 6
9 eleq2 2414 . . . . . 6
108, 9syl6 29 . . . . 5
112, 3, 5, 7, 10dvelimdf 2082 . . . 4
1211imp 418 . . 3
131, 12nfcd 2484 . 2
1413ex 423 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1540  wnf 1544   wceq 1642   wcel 1710  wnfc 2476 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  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478 This theorem is referenced by:  dvelimc  2510
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