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Theorem sbc2rexg 26882
 Description: Exchange a substitution with two existentials. (Contributed by Stefan O'Rear, 11-Oct-2014.)
Assertion
Ref Expression
sbc2rexg
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,)   ()   (,)   (,)   (,,)

Proof of Theorem sbc2rexg
StepHypRef Expression
1 elex 2970 . 2
2 sbcrexgOLD 3251 . . 3
3 sbcrexgOLD 3251 . . . 4
43rexbidv 2732 . . 3
52, 4bitrd 246 . 2
61, 5syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wcel 1727  wrex 2712  cvv 2962  wsbc 3167 This theorem is referenced by:  sbc4rexg  26883  3rexfrabdioph  26895  7rexfrabdioph  26898 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-rex 2717  df-v 2964  df-sbc 3168
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