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Theorem wl-sb6nae 33644
Description: Version of sb6 2558 suitable for elimination of unnecessary dv restrictions. (Contributed by Wolf Lammen, 28-Jul-2019.)
Assertion
Ref Expression
wl-sb6nae (¬ ∀𝑥 𝑥 = 𝑦 → ([𝑦 / 𝑥]𝜑 ↔ ∀𝑥(𝑥 = 𝑦𝜑)))

Proof of Theorem wl-sb6nae
StepHypRef Expression
1 sb4b 2487 1 (¬ ∀𝑥 𝑥 = 𝑦 → ([𝑦 / 𝑥]𝜑 ↔ ∀𝑥(𝑥 = 𝑦𝜑)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wal 1622  [wsb 2038
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878  ax-5 1980  ax-6 2046  ax-7 2082  ax-10 2160  ax-12 2188  ax-13 2383
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1846  df-nf 1851  df-sb 2039
This theorem is referenced by:  wl-2sb6d  33646
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