Theorem spesbcd 3085

Description: form of spsbc 3010. (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

Step	Hyp	Ref	Expression
1		spesbcd.1	. 2 |- ( ph -> [. A / x ]. ps )
2		spesbc 3084	. 2 |- ( [. A / x ]. ps -> E. x ps )
3	1, 2	syl 14	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1515   [.wsbc 2998

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-rex 2490  df-v 2774  df-sbc 2999

This theorem is referenced by:  euotd  4299  bj-sels  15850