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Theorem rexdifpr 39141
 Description: Restricted existential quantification over a set with two elements removed. (Contributed by Alexander van der Vekens, 7-Feb-2018.)
Assertion
Ref Expression
rexdifpr

Proof of Theorem rexdifpr
StepHypRef Expression
1 eldifpr 3982 . . . . 5
2 3anass 1011 . . . . 5
31, 2bitri 257 . . . 4
43anbi1i 709 . . 3
5 anass 661 . . . 4
6 df-3an 1009 . . . . . 6
76bicomi 207 . . . . 5
87anbi2i 708 . . . 4
95, 8bitri 257 . . 3
104, 9bitri 257 . 2
1110rexbii2 2879 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   w3a 1007   wcel 1904   wne 2641  wrex 2757   cdif 3387  cpr 3961 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-rex 2762  df-v 3033  df-dif 3393  df-un 3395  df-sn 3960  df-pr 3962 This theorem is referenced by:  usgra2pth0  40177
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