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Theorem reusv2lem1 4604
 Description: Lemma for reusv2 4609. (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 3741 . . 3
2 nfra1 2769 . . . . 5
32nfmo 2316 . . . 4
4 rsp 2754 . . . . . . 7
54com12 32 . . . . . 6
65alrimiv 1773 . . . . 5
7 moeq 3214 . . . . 5
8 moim 2348 . . . . 5
96, 7, 8mpisyl 21 . . . 4
103, 9exlimi 1995 . . 3
111, 10sylbi 199 . 2
12 eu5 2325 . . 3
1312rbaib 917 . 2
1411, 13syl 17 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188  wal 1442   wceq 1444  wex 1663   wcel 1887  weu 2299  wmo 2300   wne 2622  wral 2737  c0 3731 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-ral 2742  df-v 3047  df-dif 3407  df-nul 3732 This theorem is referenced by: (None)
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