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Theorem spesbcd 3073
Description: form of spsbc 3003. (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 3072 . 2  |-  ( [. A  /  x ]. ps  ->  E. x ps )
31, 2syl 15 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1528   [.wsbc 2991
This theorem is referenced by:  ex-natded9.26  20806
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-v 2790  df-sbc 2992
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