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Theorem spvw 1666
Description: Version of sp 1747 when x does not occur in φ. This provides the other direction of ax-17 1616. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 10-Apr-2017.) (Proof shortened by Wolf Lammen, 4-Dec-2017.)
Ref Expression
spvw (xφφ)
Distinct variable group:   φ,x

Proof of Theorem spvw
StepHypRef Expression
1 19.3v 1665 . 2 (xφφ)
21biimpi 186 1 (xφφ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by:  19.3vOLD  1696
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