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Theorem spesbcd 2990
Description: form of spsbc 2915. (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 2989 . 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 1468   [.wsbc 2904
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-v 2683  df-sbc 2905
This theorem is referenced by:  euotd  4171  bj-sels  13101
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