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Theorem spvw 1661
Description: Version of sp 1716 when  x does not occur in  ph. This provides the other direction of ax-17 1603. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 10-Apr-2017.)
Assertion
Ref Expression
spvw  |-  ( A. x ph  ->  ph )
Distinct variable group:    ph, x

Proof of Theorem spvw
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 biidd 228 . 2  |-  ( x  =  y  ->  ( ph 
<-> 
ph ) )
21spw 1660 1  |-  ( A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  19.3v  1662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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