Theorem spesbcd 3119

Description: form of spsbc 3043. (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 3118	. 2 |- ( [. A / x ]. ps -> E. x ps )
3	1, 2	syl 14	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1540   [.wsbc 3031

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rex 2516  df-v 2804  df-sbc 3032

This theorem is referenced by:  euotd  4347  bj-sels  16509