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Theorem 2rexsb 27915
 Description: An equivalent expression for double restricted existence, analogous to rexsb 27913. (Contributed by Alexander van der Vekens, 1-Jul-2017.)
Assertion
Ref Expression
2rexsb
Distinct variable groups:   ,,,,   ,,,   ,,
Allowed substitution hints:   (,)   ()

Proof of Theorem 2rexsb
StepHypRef Expression
1 rexsb 27913 . . . 4
21rexbii 2722 . . 3
3 rexcom 2861 . . 3
42, 3bitri 241 . 2
5 rexsb 27913 . . . . 5
6 impexp 434 . . . . . . . . 9
76albii 1575 . . . . . . . 8
8 19.21v 1913 . . . . . . . 8
97, 8bitr2i 242 . . . . . . 7
109albii 1575 . . . . . 6
1110rexbii 2722 . . . . 5
125, 11bitri 241 . . . 4
1312rexbii 2722 . . 3
14 rexcom 2861 . . 3
1513, 14bitri 241 . 2
164, 15bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wrex 2698 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703
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