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Theorem 2rexrsb 28052
 Description: An equivalent expression for double restricted existence, analogous to 2exsb 2084. (Contributed by Alexander van der Vekens, 1-Jul-2017.)
Assertion
Ref Expression
2rexrsb
Distinct variable groups:   ,,,,   ,,,   ,,
Allowed substitution hints:   (,)   ()

Proof of Theorem 2rexrsb
StepHypRef Expression
1 rexrsb 28050 . . . 4
21rexbii 2581 . . 3
3 rexcom 2714 . . 3
42, 3bitri 240 . 2
5 rexrsb 28050 . . . . 5
6 impexp 433 . . . . . . . . 9
76ralbii 2580 . . . . . . . 8
8 r19.21v 2643 . . . . . . . 8
97, 8bitr2i 241 . . . . . . 7
109ralbii 2580 . . . . . 6
1110rexbii 2581 . . . . 5
125, 11bitri 240 . . . 4
1312rexbii 2581 . . 3
14 rexcom 2714 . . 3
1513, 14bitri 240 . 2
164, 15bitri 240 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wral 2556  wrex 2557 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562
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