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Theorem spvw 1986
Description: Version of sp 2184 when 𝑥 does not occur in 𝜑. Converse of ax-5 1912. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 10-Apr-2017.) (Proof shortened by Wolf Lammen, 4-Dec-2017.) Shorten 19.3v 1987. (Revised by Wolf Lammen, 20-Oct-2023.)
Assertion
Ref Expression
spvw (∀𝑥𝜑𝜑)
Distinct variable group:   𝜑,𝑥

Proof of Theorem spvw
StepHypRef Expression
1 ax-5 1912 . 2 𝜑 → ∀𝑥 ¬ 𝜑)
21spnfw 1985 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by:  19.3v  1987
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