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Theorem raaanlem 3354
 Description: Special case of raaan 3355 where is inhabited. (Contributed by Jim Kingdon, 6-Aug-2018.)
Hypotheses
Ref Expression
raaan.1
raaan.2
Assertion
Ref Expression
raaanlem
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem raaanlem
StepHypRef Expression
1 eleq1 2116 . . . 4
21cbvexv 1811 . . 3
3 raaan.1 . . . . 5
43r19.28m 3339 . . . 4
54ralbidv 2343 . . 3
62, 5sylbi 118 . 2
7 nfcv 2194 . . . 4
8 raaan.2 . . . 4
97, 8nfralxy 2377 . . 3
109r19.27m 3344 . 2
116, 10bitrd 181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102  wnf 1365  wex 1397   wcel 1409  wral 2323 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328 This theorem is referenced by:  raaan  3355
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