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Theorem spvw 1655
Description: Version of sp 1728 when  x does not occur in  ph. This provides the other direction of ax-17 1606. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 10-Apr-2017.) (Proof shortened by Wolf Lammen, 4-Dec-2017.)
Assertion
Ref Expression
spvw  |-  ( A. x ph  ->  ph )
Distinct variable group:    ph, x

Proof of Theorem spvw
StepHypRef Expression
1 19.3v 1654 . 2  |-  ( A. x ph  <->  ph )
21biimpi 186 1  |-  ( A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530
This theorem is referenced by:  19.3vOLD  1681
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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