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Theorem spesbcd 2925
Description: form of spsbc 2851. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
spesbcd.1  |-  ( ph  ->  [. A  /  x ]. ps )
Assertion
Ref Expression
spesbcd  |-  ( ph  ->  E. x ps )

Proof of Theorem spesbcd
StepHypRef Expression
1 spesbcd.1 . 2  |-  ( ph  ->  [. A  /  x ]. ps )
2 spesbc 2924 . 2  |-  ( [. A  /  x ]. ps  ->  E. x ps )
31, 2syl 14 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1426   [.wsbc 2840
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-sbc 2841
This theorem is referenced by:  euotd  4081  bj-sels  11760
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