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Theorem spesbcd 3207
Description: form of spsbc 3137. (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 3206 . 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 1547   [.wsbc 3125
This theorem is referenced by:  euotd  4421  ex-natded9.26  21684  bnj1465  28926
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ral 2675  df-rex 2676  df-v 2922  df-sbc 3126
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