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Theorem spesbc 3127
Description: Existence form of spsbc 3058. (Contributed by Mario Carneiro, 18-Nov-2016.)
Assertion
Ref Expression
spesbc  [.  ].

Proof of Theorem spesbc
StepHypRef Expression
1 sbcex 3055 . . 3  [.  ].
2 rspesbca 3126 . . 3  [.  ].
31, 2mpancom 650 . 2  [.  ].
4 rexv 2873 . 2
53, 4sylib 188 1  [.  ].
Colors of variables: wff setvar class
Syntax hints:   wi 4  wex 1541   wcel 1710  wrex 2615  cvv 2859   [.wsbc 3046
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047
This theorem is referenced by:  spesbcd  3128  opelopabsb  4697
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