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Theorem reusv2lem1 4724
 Description: Lemma for reusv2 4729. (Contributed by NM, 22-Oct-2010.) (Proof shortened by Mario Carneiro, 19-Nov-2016.)
Assertion
Ref Expression
reusv2lem1
Distinct variable groups:   ,,   ,
Allowed substitution hint:   ()

Proof of Theorem reusv2lem1
StepHypRef Expression
1 n0 3637 . . 3
2 nfra1 2756 . . . . 5
32nfmo 2298 . . . 4
4 rsp 2766 . . . . . . 7
54com12 29 . . . . . 6
65alrimiv 1641 . . . . 5
7 moeq 3110 . . . . 5
8 moim 2327 . . . . 5
96, 7, 8ee10 1385 . . . 4
103, 9exlimi 1821 . . 3
111, 10sylbi 188 . 2
12 eu5 2319 . . 3
1312rbaib 874 . 2
1411, 13syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549  wex 1550   wceq 1652   wcel 1725  weu 2281  wmo 2282   wne 2599  wral 2705  c0 3628 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 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-v 2958  df-dif 3323  df-nul 3629
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