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Theorem spvw 1824
Description: Version of sp 1947 when  x does not occur in  ph. Converse of ax-5 1768. 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 1823 . 2  |-  ( A. x ph  <->  ph )
21biimpi 199 1  |-  ( A. x ph  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815
This theorem depends on definitions:  df-bi 190  df-ex 1674
This theorem is referenced by: (None)
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