Theorem spesbcd 3116

Description: form of spsbc 3040. (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 3115	. 2 |- ( [. A / x ]. ps -> E. x ps )
3	1, 2	syl 14	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1538   [.wsbc 3028

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-rex 2514  df-v 2801  df-sbc 3029

This theorem is referenced by:  euotd  4341  bj-sels  16277