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Theorem spnfw 1974
Description: Weak version of sp 2091. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 13-Aug-2017.)
Hypothesis
Ref Expression
spnfw.1 𝜑 → ∀𝑥 ¬ 𝜑)
Assertion
Ref Expression
spnfw (∀𝑥𝜑𝜑)

Proof of Theorem spnfw
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 spnfw.1 . 2 𝜑 → ∀𝑥 ¬ 𝜑)
2 idd 24 . 2 (𝑥 = 𝑦 → (𝜑𝜑))
31, 2spimw 1972 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  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-6 1945
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by:  spfalw  1975
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