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Theorem spesbc 3420
Description: Existence form of spsbc 3340. (Contributed by Mario Carneiro, 18-Nov-2016.)
Assertion
Ref Expression
spesbc

Proof of Theorem spesbc
StepHypRef Expression
1 sbcex 3337 . . 3
2 rspesbca 3419 . . 3
31, 2mpancom 669 . 2
4 rexv 3124 . 2
53, 4sylib 196 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  E.wex 1612  e.wcel 1818  E.wrex 2808   cvv 3109  [.wsbc 3327
This theorem is referenced by:  spesbcd  3421  opelopabsb  4762  sbccomieg  30726  sbiota1  31341
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328
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