Theorem spesbcd 3120

Description: form of spsbc 3044. (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 3119	. 2 |- ( [. A / x ]. ps -> E. x ps )
3	1, 2	syl 14	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1541   [.wsbc 3032

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-rex 2517  df-v 2805  df-sbc 3033

This theorem is referenced by:  euotd  4353  bj-sels  16630