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Theorem rexrsb 27914
 Description: An equivalent expression for restricted existence, analogous to exsb 2206. (Contributed by Alexander van der Vekens, 1-Jul-2017.)
Assertion
Ref Expression
rexrsb
Distinct variable groups:   ,,   ,
Allowed substitution hint:   ()

Proof of Theorem rexrsb
StepHypRef Expression
1 rexsb 27913 . 2
2 alral 2756 . . . 4
3 df-ral 2702 . . . . . 6
4 19.27v 1917 . . . . . . . 8
5 pm2.04 78 . . . . . . . . . . 11
6 eleq1 2495 . . . . . . . . . . . . 13
76biimprd 215 . . . . . . . . . . . 12
8 pm2.83 73 . . . . . . . . . . . 12
97, 8ax-mp 8 . . . . . . . . . . 11
10 pm2.04 78 . . . . . . . . . . 11
115, 9, 103syl 19 . . . . . . . . . 10
1211imp 419 . . . . . . . . 9
1312alimi 1568 . . . . . . . 8
144, 13sylbir 205 . . . . . . 7
1514ex 424 . . . . . 6
163, 15sylbi 188 . . . . 5
1716com12 29 . . . 4
182, 17impbid2 196 . . 3
1918rexbiia 2730 . 2
201, 19bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wcel 1725  wral 2697  wrex 2698 This theorem is referenced by:  2rexrsb  27916 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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