Theorem spsbe 1884

Description: A specialization theorem. (Contributed by NM, 29-Jun-1993.) (Proof shortened by Wolf Lammen, 3-May-2018.)

Assertion

Ref	Expression
spsbe	|- ( [ y / x ] ph -> E. x ph )

Proof of Theorem spsbe

Step	Hyp	Ref	Expression
1		sb1 1883	. 2 |- ( [ y / x ] ph -> E. x ( x = y /\ ph ) )
2		exsimpr 1796	. 2 |- ( E. x ( x = y /\ ph ) -> E. x ph )
3	1, 2	syl 17	1 |- ( [ y / x ] ph -> E. x ph )

Syntax hints:   -> wi 4   /\ wa 384   E.wex 1704   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-sb 1881

This theorem is referenced by:  sbft  2379  2mo  2551  bj-sbftv  32763  bj-sbfvv  32765  wl-lem-moexsb  33350  spsbce-2  38580  sb5ALT  38731  sb5ALTVD  39149