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Theorem spesbcd 3245
Description: form of spsbc 3175. (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 3244 . 2  |-  ( [. A  /  x ]. ps  ->  E. x ps )
31, 2syl 16 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1551   [.wsbc 3163
This theorem is referenced by:  euotd  4460  ex-natded9.26  21732  bnj1465  29290
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 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
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 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-sbc 3164
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