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Theorem spvw 1955
Description: Version of sp 2091 when 𝑥 does not occur in 𝜑. Converse of ax-5 1879. 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 (∀𝑥𝜑𝜑)
Distinct variable group:   𝜑,𝑥

Proof of Theorem spvw
StepHypRef Expression
1 19.3v 1954 . 2 (∀𝑥𝜑𝜑)
21biimpi 206 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by: (None)
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