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Theorem spsbe 1663
Description: A specialization theorem. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-May-2018.)
Assertion
Ref Expression
spsbe  |-  ( [ y  /  x ] ph  ->  E. x ph )

Proof of Theorem spsbe
StepHypRef Expression
1 sb1 1662 . 2  |-  ( [ y  /  x ] ph  ->  E. x ( x  =  y  /\  ph ) )
2 simpr 448 . . 3  |-  ( ( x  =  y  /\  ph )  ->  ph )
32eximi 1585 . 2  |-  ( E. x ( x  =  y  /\  ph )  ->  E. x ph )
41, 3syl 16 1  |-  ( [ y  /  x ] ph  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359   E.wex 1550   [wsb 1658
This theorem is referenced by:  sbft  2115  spsbce-2  27556  sb5ALT  28609  sb5ALTVD  29025
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-sb 1659
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