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Theorem rexim 2413
 Description: Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Nov-1994.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Assertion
Ref Expression
rexim

Proof of Theorem rexim
StepHypRef Expression
1 df-ral 2311 . . . 4
2 simpl 102 . . . . . . 7
32a1i 9 . . . . . 6
4 pm3.31 249 . . . . . 6
53, 4jcad 291 . . . . 5
65alimi 1344 . . . 4
71, 6sylbi 114 . . 3
8 exim 1490 . . 3
97, 8syl 14 . 2
10 df-rex 2312 . 2
11 df-rex 2312 . 2
129, 10, 113imtr4g 194 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97  wal 1241  wex 1381   wcel 1393  wral 2306  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-ral 2311  df-rex 2312 This theorem is referenced by:  reximia  2414  reximdai  2417  r19.29  2450  reupick2  3223  ss2iun  3672  chfnrn  5278
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