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Theorem dvelimdc 2591
 Description: Deduction form of dvelimc 2592. (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 1629 . . 3
2 dvelimdc.1 . . . . 5
3 dvelimdc.2 . . . . 5
4 dvelimdc.3 . . . . . 6
54nfcrd 2584 . . . . 5
6 dvelimdc.4 . . . . . 6
76nfcrd 2584 . . . . 5
8 dvelimdc.5 . . . . . 6
9 eleq2 2496 . . . . . 6
108, 9syl6 31 . . . . 5
112, 3, 5, 7, 10dvelimdf 2066 . . . 4
1211imp 419 . . 3
131, 12nfcd 2566 . 2
1413ex 424 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1549  wnf 1553   wceq 1652   wcel 1725  wnfc 2558 This theorem is referenced by:  dvelimc  2592 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-cleq 2428  df-clel 2431  df-nfc 2560
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