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Theorem ralnex 2310
Description: Relationship between restricted universal and existential quantifiers. (Contributed by NM, 21-Jan-1997.)
Assertion
Ref Expression
ralnex

Proof of Theorem ralnex
StepHypRef Expression
1 df-ral 2305 . 2
2 alinexa 1491 . . 3
3 df-rex 2306 . . 3
42, 3xchbinxr 607 . 2
51, 4bitri 173 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wb 98  wal 1240  wex 1378   wcel 1390  wral 2300  wrex 2301
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-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie2 1380
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-ral 2305  df-rex 2306
This theorem is referenced by:  rexalim  2313  ralinexa  2345  nrex  2405  nrexdv  2406  uni0b  3596  iindif2m  3715  icc0r  8525
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