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Theorem dvelimdc 2642
 Description: Deduction form of dvelimc 2643. (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 1707 . . 3
2 dvelimdc.1 . . . . 5
3 dvelimdc.2 . . . . 5
4 dvelimdc.3 . . . . . 6
54nfcrd 2625 . . . . 5
6 dvelimdc.4 . . . . . 6
76nfcrd 2625 . . . . 5
8 dvelimdc.5 . . . . . 6
9 eleq2 2530 . . . . . 6
108, 9syl6 33 . . . . 5
112, 3, 5, 7, 10dvelimdf 2077 . . . 4
1211imp 429 . . 3
131, 12nfcd 2613 . 2
1413ex 434 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605 This theorem is referenced by:  dvelimc  2643 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-nfc 2607
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