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Theorem rexn0 3356
 Description: Restricted existential quantification implies its restriction is nonempty (it is also inhabited as shown in rexm 3357). (Contributed by Szymon Jaroszewicz, 3-Apr-2007.)
Assertion
Ref Expression
rexn0
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rexn0
StepHypRef Expression
1 ne0i 3273 . . 3
21a1d 22 . 2
32rexlimiv 2476 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1434   wne 2249  wrex 2354  c0 3267 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ne 2250  df-ral 2358  df-rex 2359  df-v 2612  df-dif 2984  df-nul 3268 This theorem is referenced by: (None)
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