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Theorem 3reeanv 2474
Description: Rearrange three existential quantifiers. (Contributed by Jeff Madsen, 11-Jun-2010.)
Assertion
Ref Expression
3reeanv  C  C
Distinct variable groups:   ,,   ,,   ,,   ,   ,,   , C,
Allowed substitution hints:   ()   ()   ()   (,)   ()    C()

Proof of Theorem 3reeanv
StepHypRef Expression
1 r19.41v 2460 . . 3  C  C
2 reeanv 2473 . . . 4
32anbi1i 431 . . 3  C  C
41, 3bitri 173 . 2  C  C
5 df-3an 886 . . . . 5
652rexbii 2327 . . . 4  C  C
7 reeanv 2473 . . . 4  C  C
86, 7bitri 173 . . 3  C  C
98rexbii 2325 . 2  C  C
10 df-3an 886 . 2  C  C
114, 9, 103bitr4i 201 1  C  C
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   w3a 884  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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306
This theorem is referenced by: (None)
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